메뉴 건너뛰기




Volumn PartF1, Issue , 2013, Pages 1-182

Regular functions of a quaternionic variable

Author keywords

[No Author keywords available]

Indexed keywords


EID: 85084168098     PISSN: 14397382     EISSN: 21969922     Source Type: Book Series    
DOI: 10.1007/978-3-642-33871-7     Document Type: Chapter
Times cited : (2195)

References (130)
  • 2
    • 0003787245 scopus 로고
    • Quaternionic quantum mechanics and quantum fields
    • vol., The Clarendon Press/Oxford University Press, New York
    • S.L. Adler, Quaternionic quantum mechanics and quantum fields. International Series of Monographs on Physics, vol. 88 (The Clarendon Press/Oxford University Press, New York, 1995)
    • (1995) International Series of Monographs on Physics , vol.88
    • Adler, S.L.1
  • 3
    • 84968508888 scopus 로고
    • On Phragmén-Lindelöf’s principle
    • L.V. Ahlfors, On Phragmén-Lindelöf’s principle. Trans. Am. Math. Soc. 41(1), 1–8 (1937)
    • (1937) Trans. Am. Math. Soc. , vol.41 , Issue.1 , pp. 1-8
    • Ahlfors, L.V.1
  • 7
    • 77949804703 scopus 로고    scopus 로고
    • Möbius transformations and the Poincaré distance in the quaternionic setting
    • C. Bisi, G. Gentili, Möbius transformations and the Poincaré distance in the quaternionic setting. Indiana Univ. Math. J. 58(6), 2729–2764 (2009)
    • (2009) Indiana Univ. Math. J. , vol.58 , Issue.6 , pp. 2729-2764
    • Bisi, C.1    Gentili, G.2
  • 8
    • 84959209854 scopus 로고    scopus 로고
    • On the geometry of the quaternionic unit disc
    • ed. by I. Sabadini, F. Sommen. Trends in Mathematics (Birkhäuser Basel, ), pp
    • C. Bisi, G. Gentili, On the geometry of the quaternionic unit disc, in Hypercomplex Analysis and Applications, ed. by I. Sabadini, F. Sommen. Trends in Mathematics (Birkhäuser Basel, 2011), pp. 1–11
    • (2011) Hypercomplex Analysis and Applications , pp. 1-11
    • Bisi, C.1    Gentili, G.2
  • 9
    • 84877711233 scopus 로고    scopus 로고
    • The Schwarz-Pick lemma for slice regular functions
    • C. Bisi, C. Stoppato, The Schwarz-Pick lemma for slice regular functions. Indiana Univ. Math. J., doi:101512/iumj.2012.61.5076
    • Indiana Univ. Math. J.
    • Bisi, C.1    Stoppato, C.2
  • 10
    • 85015593637 scopus 로고    scopus 로고
    • Regular vs. Classical Möbius transformations of the quaternionic unit ball
    • ed. by G. Gentili, I. Sabadini, M.V. Shapiro, F. Sommen, D.C. Struppa. Springer INdAM Series (Springer, Milan, ), pp
    • C. Bisi, C. Stoppato, Regular vs. classical Möbius transformations of the quaternionic unit ball, in Advances in Hypercomplex Analysis, ed. by G. Gentili, I. Sabadini, M.V. Shapiro, F. Sommen, D.C. Struppa. Springer INdAM Series (Springer, Milan, 2013), pp. 1–13
    • (2013) Advances in Hypercomplex Analysis , pp. 1-13
    • Bisi, C.1    Stoppato, C.2
  • 12
    • 0002599309 scopus 로고
    • A theorem concerning power series
    • H. Bohr, A theorem concerning power series. Proc. Lond. Math. Soc. S2-13(1), 1–5 (1914)
    • (1914) Proc. Lond. Math. Soc. , vol.13 , Issue.1 , pp. 1-5
    • Bohr, H.1
  • 14
    • 84968468477 scopus 로고
    • Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary
    • D.M. Burns, S.G. Krantz, Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary. J. Am. Math. Soc. 7(3), 661–676 (1994)
    • (1994) J. Am. Math. Soc. , vol.7 , Issue.3 , pp. 661-676
    • Burns, D.M.1    Krantz, S.G.2
  • 15
    • 0000045888 scopus 로고
    • Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications
    • H. Cartan, Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications. Ann. Sci. École Norm. Sup. (3) 45, 255–346 (1928)
    • (1928) Ann. Sci. École Norm. Sup. , vol.45 , Issue.3 , pp. 255-346
    • Cartan, H.1
  • 16
    • 34247570467 scopus 로고
    • An Introduction to Clifford Analysis. Textos de Matemática
    • vol., Universidade de Coimbra Departamento de Matemática, Coimbra
    • J. Cnops, H. Malonek, An Introduction to Clifford Analysis. Textos de Matemática. Série B, vol. 7 (Universidade de Coimbra Departamento de Matemática, Coimbra, 1995)
    • (1995) Série B , vol.7
    • Cnops, J.1    Malonek, H.2
  • 18
  • 19
    • 69849112059 scopus 로고    scopus 로고
    • Extension results for slice regular functions of a quaternionic variable
    • F. Colombo, G. Gentili, I. Sabadini, D. Struppa, Extension results for slice regular functions of a quaternionic variable. Adv. Math. 222(5), 1793–1808 (2009)
    • (2009) Adv. Math. , vol.222 , Issue.5 , pp. 1793-1808
    • Colombo, F.1    Gentili, G.2    Sabadini, I.3    Struppa, D.4
  • 21
    • 79953650659 scopus 로고    scopus 로고
    • An overview on functional calculus in different settings
    • in Hypercomplex Analysis, ed., I. Sabadini, M.V. Shapiro, F. Sommen, Birkhäuser, Basel, ), pp
    • F. Colombo, G. Gentili, I. Sabadini, D.C. Struppa, An overview on functional calculus in different settings, in Hypercomplex Analysis, ed. by I. Sabadini, M.V. Shapiro, F. Sommen. Trends in Mathematics (Birkhäuser, Basel, 2009), pp. 69–99
    • (2009) Trends in Mathematics , pp. 69-99
    • Colombo, F.1    Gentili, G.2    Sabadini, I.3    Struppa, D.C.4
  • 23
    • 74149087260 scopus 로고    scopus 로고
    • Non-commutative functional calculus: Unbounded operators
    • F. Colombo, G. Gentili, I. Sabadini, D.C. Struppa, Non-commutative functional calculus: Unbounded operators. J. Geom. Phys. 60(2), 251–259 (2010)
    • (2010) J. Geom. Phys. , vol.60 , Issue.2 , pp. 251-259
    • Colombo, F.1    Gentili, G.2    Sabadini, I.3    Struppa, D.C.4
  • 24
    • 79953660108 scopus 로고    scopus 로고
    • On some properties of the quaternionic functional calculus
    • F. Colombo, I. Sabadini, On some properties of the quaternionic functional calculus. J. Geom. Anal. 19(3), 601–627 (2009)
    • (2009) J. Geom. Anal. , vol.19 , Issue.3 , pp. 601-627
    • Colombo, F.1    Sabadini, I.2
  • 25
    • 84959102965 scopus 로고    scopus 로고
    • A structure formula for slice monogenic functions and some of its consequences
    • in Hypercomplex Analysis, ed., I. Sabadini, M. Shapiro, F. Sommen., Birkhäuser, Basel, ), pp
    • F. Colombo, I. Sabadini, A structure formula for slice monogenic functions and some of its consequences, in Hypercomplex Analysis, ed. by I. Sabadini, M. Shapiro, F. Sommen. Trends in Mathematics (Birkhäuser, Basel, 2009), pp. 101–114
    • (2009) Trends in Mathematics , pp. 101-114
    • Colombo, F.1    Sabadini, I.2
  • 26
    • 77954377621 scopus 로고    scopus 로고
    • On the formulations of the quaternionic functional calculus
    • F. Colombo, I. Sabadini, On the formulations of the quaternionic functional calculus. J. Geom. Phys. 60(10), 1490–1508 (2010)
    • (2010) J. Geom. Phys. , vol.60 , Issue.10 , pp. 1490-1508
    • Colombo, F.1    Sabadini, I.2
  • 27
    • 77956610959 scopus 로고    scopus 로고
    • The Cauchy formula with s-monogenic kernel and a functional calculus for noncommuting operators
    • F. Colombo, I. Sabadini, The Cauchy formula with s-monogenic kernel and a functional calculus for noncommuting operators. J. Math. Anal. Appl. 373(2), 655–679 (2011)
    • (2011) J. Math. Anal. Appl. , vol.373 , Issue.2 , pp. 655-679
    • Colombo, F.1    Sabadini, I.2
  • 28
    • 79956359162 scopus 로고    scopus 로고
    • The quaternionic evolution operator
    • F. Colombo, I. Sabadini, The quaternionic evolution operator. Adv. Math. 227(5), 1772–1805 (2011)
    • (2011) Adv. Math. , vol.227 , Issue.5 , pp. 1772-1805
    • Colombo, F.1    Sabadini, I.2
  • 29
    • 84860837849 scopus 로고    scopus 로고
    • The F-spectrum and the SC-functional calculus
    • F. Colombo, I. Sabadini, The F-spectrum and the SC-functional calculus. Proc. Roy. Soc. Edinb. Sect. A 142(3), 479–500 (2012)
    • (2012) Proc. Roy. Soc. Edinb. Sect. A , vol.142 , Issue.3 , pp. 479-500
    • Colombo, F.1    Sabadini, I.2
  • 30
    • 84958987417 scopus 로고    scopus 로고
    • An invitation to the S-functional calculus
    • ed. by W. Arendt, J.A. Ball, J. Behrndt, K.-H. Förster, V. Mehrmann, C. Trunk. Operator Theory: Advances and Applications, vol., Springer, Basel, ), pp
    • F. Colombo, I. Sabadini, An invitation to the S-functional calculus, in Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, ed. by W. Arendt, J.A. Ball, J. Behrndt, K.-H. Förster, V. Mehrmann, C. Trunk. Operator Theory: Advances and Applications, vol. 221 (Springer, Basel, 2012), pp. 241–254
    • (2012) Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations , vol.221 , pp. 241-254
    • Colombo, F.1    Sabadini, I.2
  • 31
    • 78649586367 scopus 로고    scopus 로고
    • The Fueter mapping theorem in integral form and the F-functional calculus
    • F. Colombo, I. Sabadini, F. Sommen, The Fueter mapping theorem in integral form and the F-functional calculus. Math. Meth. Appl. Sci. 33(17), 2050–2066 (2010)
    • (2010) Math. Meth. Appl. Sci. , vol.33 , Issue.17 , pp. 2050-2066
    • Colombo, F.1    Sabadini, I.2    Sommen, F.3
  • 35
    • 77954381128 scopus 로고    scopus 로고
    • An extension theorem for slice monogenic functions and some of its consequences
    • F. Colombo, I. Sabadini, D.C. Struppa, An extension theorem for slice monogenic functions and some of its consequences. Isr. J. Math. 177, 369–389 (2010)
    • (2010) Isr. J. Math. , vol.177 , pp. 369-389
    • Colombo, F.1    Sabadini, I.2    Struppa, D.C.3
  • 36
    • 85028031040 scopus 로고    scopus 로고
    • Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions
    • vol., Birkhäuser/Springer, Basel
    • F. Colombo, I. Sabadini, D.C. Struppa, Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions. Progress in Mathematics, vol. 289 (Birkhäuser/Springer, Basel, 2011)
    • (2011) Progress in Mathematics , vol.289
    • Colombo, F.1    Sabadini, I.2    Struppa, D.C.3
  • 37
    • 79953658772 scopus 로고    scopus 로고
    • The Pompeiu formula for slice hyperholomorphic functions
    • F. Colombo, I. Sabadini, D.C. Struppa, The Pompeiu formula for slice hyperholomorphic functions. Mich. Math. J. 60(1), 163–170 (2011)
    • (2011) Mich. Math. J. , vol.60 , Issue.1 , pp. 163-170
    • Colombo, F.1    Sabadini, I.2    Struppa, D.C.3
  • 38
    • 0003499337 scopus 로고
    • Functions of one complex variable
    • vol., 2nd edn. (Springer, New York
    • J.B. Conway, Functions of one complex variable. Graduate Texts in Mathematics, vol. 11, 2nd edn. (Springer, New York, 1978)
    • (1978) Graduate Texts in Mathematics , vol.11
    • Conway, J.B.1
  • 39
    • 84972537470 scopus 로고
    • An integral theorem for analytic intrinsic functions on quaternions
    • C.G. Cullen, An integral theorem for analytic intrinsic functions on quaternions. Duke Math. J. 32, 139–148 (1965)
    • (1965) Duke Math. J. , vol.32 , pp. 139-148
    • Cullen, C.G.1
  • 40
    • 70349445430 scopus 로고    scopus 로고
    • Computations in the ring of quaternionic polynomials
    • A. Damiano, G. Gentili, D. Struppa, Computations in the ring of quaternionic polynomials. J. Symbolic Comput. 45(1), 38–45 (2010)
    • (2010) J. Symbolic Comput. , vol.45 , Issue.1 , pp. 38-45
    • Damiano, A.1    Gentili, G.2    Struppa, D.3
  • 41
    • 84939952425 scopus 로고    scopus 로고
    • A Bloch-Landau theorem for slice regular functions
    • ed. by G. Gentili, I. Sabadini, M.V. Shapiro, F. Sommen, D.C. Struppa. Springer INdAM Series (Springer, Milan, ), pp
    • C. Della Rocchetta, G. Gentili, G. Sarfatti, A Bloch-Landau theorem for slice regular functions, in Advances in Hypercomplex Analysis, ed. by G. Gentili, I. Sabadini, M.V. Shapiro, F. Sommen, D.C. Struppa. Springer INdAM Series (Springer, Milan, 2013), pp. 55–74
    • (2013) Advances in Hypercomplex Analysis , pp. 55-74
    • della Rocchetta, C.1    Gentili, G.2    Sarfatti, G.3
  • 42
    • 84870447367 scopus 로고    scopus 로고
    • The Bohr theorem for slice regular functions
    • C. Della Rocchetta, G. Gentili, G. Sarfatti, The Bohr theorem for slice regular functions. Math. Nachr. 285(17–18), 2093–2105 (2012)
    • (2012) Math. Nachr. , vol.285 , Issue.17-18 , pp. 2093-2105
    • della Rocchetta, C.1    Gentili, G.2    Sarfatti, G.3
  • 43
    • 0010188322 scopus 로고
    • Funzioni regolari nell’algebra di Cayley
    • P. Dentoni, M. Sce, Funzioni regolari nell’algebra di Cayley. Rend. Sem. Mat. Univ. Padova 50, 251–267 (1973/1974)
    • (1973) Rend. Sem. Mat. Univ. Padova , vol.50 , pp. 251-267
    • Dentoni, P.1    Sce, M.2
  • 45
    • 0003197047 scopus 로고
    • Linear Operators. I. General Theory. With the assistance of W. G. Bade and R. G. Bartle
    • vol., Interscience Publishers, Inc., New York
    • N. Dunford, J.T. Schwartz, Linear Operators. I. General Theory. With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, vol. 7 (Interscience Publishers, Inc., New York, 1958)
    • (1958) Pure and Applied Mathematics , vol.7
    • Dunford, N.1    Schwartz, J.T.2
  • 46
    • 85084168219 scopus 로고    scopus 로고
    • (Springer, New York, 1990). With an introduction by K. Lamotke, Translated from the second German edition by H.L.S. Orde, Translation edited and with a preface by J.H. Ewing, Readings in Mathematics
    • H.-D. Ebbinghaus, H. Hermes, F. Hirzebruch, M. Koecher, K. Mainzer, J. Neukirch, A. Prestel, R. Remmert, Numbers. Graduate Texts in Mathematics, vol. 123 (Springer, New York, 1990). With an introduction by K. Lamotke, Translated from the second German edition by H.L.S. Orde, Translation edited and with a preface by J.H. Ewing, Readings in Mathematics
    • Numbers. Graduate Texts in Mathematics , vol.123
    • Ebbinghaus, H.-D.1    Hermes, H.2    Hirzebruch, F.3    Koecher, M.4    Mainzer, K.5    Neukirch, J.6    Prestel, A.7    Remmert, R.8
  • 47
    • 0004173776 scopus 로고
    • Fourier analysis in several complex variables
    • vol., Wiley-Interscience, New York
    • L. Ehrenpreis, Fourier analysis in several complex variables. Pure and Applied Mathematics, vol. XVII (Wiley-Interscience, New York, 1970)
    • (1970) Pure and Applied Mathematics , vol.17
    • Ehrenpreis, L.1
  • 48
    • 84966210624 scopus 로고
    • The “fundamental theorem of algebra” for quaternions
    • S. Eilenberg, I. Niven, The “fundamental theorem of algebra” for quaternions. Bull. Am. Math. Soc. 50, 246–248 (1944)
    • (1944) Bull. Am. Math. Soc. , vol.50 , pp. 246-248
    • Eilenberg, S.1    Niven, I.2
  • 50
    • 33847603339 scopus 로고
    • Die Funktionentheorie der Differentialgleichungen u D 0 und u D 0 mit vier reellen Variablen
    • R. Fueter, Die Funktionentheorie der Differentialgleichungen u D 0 und u D 0 mit vier reellen Variablen. Comment. Math. Helv. 7(1), 307–330 (1934)
    • (1934) Comment. Math. Helv. , vol.7 , Issue.1 , pp. 307-330
    • Fueter, R.1
  • 51
    • 0001126607 scopus 로고
    • Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen
    • R. Fueter, Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen. Comment. Math. Helv. 8(1), 371–378 (1935)
    • (1935) Comment. Math. Helv. , vol.8 , Issue.1 , pp. 371-378
    • Fueter, R.1
  • 52
    • 0037835318 scopus 로고
    • Die Theorie der regulären Funktionen einer Quaternionenvariablen
    • vol., Brøggers, Oslo, ), pp
    • R. Fueter, Die Theorie der regulären Funktionen einer Quaternionenvariablen, in Comptes Rendus du Congrès International des Mathématiciens, Oslo 1936, vol. 1 (Brøggers, Oslo, 1937), pp. 75–91
    • (1937) Comptes Rendus Du Congrès International Des Mathématiciens, Oslo 1936 , vol.1 , pp. 75-91
    • Fueter, R.1
  • 55
    • 59949087387 scopus 로고    scopus 로고
    • Zeros of regular functions and polynomials of a quaternionic variable
    • G. Gentili, C. Stoppato, Zeros of regular functions and polynomials of a quaternionic variable. Mich. Math. J. 56(3), 655–667 (2008)
    • (2008) Mich. Math. J. , vol.56 , Issue.3 , pp. 655-667
    • Gentili, G.1    Stoppato, C.2
  • 56
    • 77952728943 scopus 로고    scopus 로고
    • The open mapping theorem for regular quaternionic functions
    • G. Gentili, C. Stoppato, The open mapping theorem for regular quaternionic functions. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) VIII(4), 805–815 (2009)
    • (2009) Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) , vol.8 , Issue.4 , pp. 805-815
    • Gentili, G.1    Stoppato, C.2
  • 57
    • 84863564599 scopus 로고    scopus 로고
    • The zero sets of slice regular functions and the open mapping theorem
    • ed. by I. Sabadini, F. Sommen. Trends in Mathematics (Birkhäuser, Basel, 2011)
    • G. Gentili, C. Stoppato, The zero sets of slice regular functions and the open mapping theorem, in Hypercomplex Analysis and Applications, ed. by I. Sabadini, F. Sommen. Trends in Mathematics (Birkhäuser, Basel, 2011), pp. 95–107
    • Hypercomplex Analysis and Applications , pp. 95-107
    • Gentili, G.1    Stoppato, C.2
  • 58
    • 84855208933 scopus 로고    scopus 로고
    • Power series and analyticity over the quaternions
    • G. Gentili, C. Stoppato, Power series and analyticity over the quaternions. Math. Ann. 352(1), 113–131 (2012)
    • (2012) Math. Ann. , vol.352 , Issue.1 , pp. 113-131
    • Gentili, G.1    Stoppato, C.2
  • 60
    • 84959151044 scopus 로고    scopus 로고
    • Recent developments for regular functions of a hypercomplex variable
    • in Hypercomplex Analysis, ed., I. Sabadini, M.V. Shapiro, F. Sommen, Birkhäuser, Basel, ), pp
    • G. Gentili, C. Stoppato, D.C. Struppa, F. Vlacci, Recent developments for regular functions of a hypercomplex variable, in Hypercomplex Analysis, ed. by I. Sabadini, M.V. Shapiro, F. Sommen. Trends in Mathematics (Birkhäuser, Basel, 2009), pp. 165–185
    • (2009) Trends in Mathematics , pp. 165-185
    • Gentili, G.1    Stoppato, C.2    Struppa, D.C.3    Vlacci, F.4
  • 61
    • 33748137777 scopus 로고    scopus 로고
    • A new approach to Cullen-regular functions of a quaternionic variable
    • G. Gentili, D.C. Struppa, A new approach to Cullen-regular functions of a quaternionic variable. C. R. Math. Acad. Sci. Paris 342(10), 741–744 (2006)
    • (2006) C. R. Math. Acad. Sci. Paris , vol.342 , Issue.10 , pp. 741-744
    • Gentili, G.1    Struppa, D.C.2
  • 62
    • 34548156026 scopus 로고    scopus 로고
    • A new theory of regular functions of a quaternionic variable
    • G. Gentili, D.C. Struppa, A new theory of regular functions of a quaternionic variable. Adv. Math. 216(1), 279–301 (2007)
    • (2007) Adv. Math. , vol.216 , Issue.1 , pp. 279-301
    • Gentili, G.1    Struppa, D.C.2
  • 63
    • 58149149747 scopus 로고    scopus 로고
    • On the multiplicity of zeroes of polynomials with quaternionic coefficients
    • G. Gentili, D.C. Struppa, On the multiplicity of zeroes of polynomials with quaternionic coefficients. Milan J. Math. 76, 15–25 (2008)
    • (2008) Milan J. Math. , vol.76 , pp. 15-25
    • Gentili, G.1    Struppa, D.C.2
  • 64
    • 77749298066 scopus 로고    scopus 로고
    • Regular functions on a Clifford algebra
    • G. Gentili, D.C. Struppa, Regular functions on a Clifford algebra. Complex Var. Elliptic Equat. 53(5), 475–483 (2008)
    • (2008) Complex Var. Elliptic Equat. , vol.53 , Issue.5 , pp. 475-483
    • Gentili, G.1    Struppa, D.C.2
  • 65
    • 77952615140 scopus 로고    scopus 로고
    • Regular functions on the space of Cayley numbers
    • G. Gentili, D.C. Struppa, Regular functions on the space of Cayley numbers. Rocky Mt. J. Math. 40(1), 225–241 (2010)
    • (2010) Rocky Mt. J. Math. , vol.40 , Issue.1 , pp. 225-241
    • Gentili, G.1    Struppa, D.C.2
  • 67
    • 84856194407 scopus 로고    scopus 로고
    • Lower bounds for polynomials of a quaternionic variable
    • G. Gentili, D.C. Struppa, Lower bounds for polynomials of a quaternionic variable. Proc. Am. Math. Soc. 140(5), 1659–1668 (2012)
    • (2012) Proc. Am. Math. Soc. , vol.140 , Issue.5 , pp. 1659-1668
    • Gentili, G.1    Struppa, D.C.2
  • 68
    • 43749083475 scopus 로고    scopus 로고
    • The fundamental theorem of algebra for Hamilton and Cayley numbers
    • G. Gentili, D.C. Struppa, F. Vlacci, The fundamental theorem of algebra for Hamilton and Cayley numbers. Math. Z. 259(4), 895–902 (2008)
    • (2008) Math. Z. , vol.259 , Issue.4 , pp. 895-902
    • Gentili, G.1    Struppa, D.C.2    Vlacci, F.3
  • 69
    • 80053132992 scopus 로고    scopus 로고
    • The Weierstrass factorization theorem for slice regular functions over the quaternions
    • G. Gentili, I. Vignozzi, The Weierstrass factorization theorem for slice regular functions over the quaternions. Ann. Global Anal. Geom. 40(4), 435–466 (2011)
    • (2011) Ann. Global Anal. Geom. , vol.40 , Issue.4 , pp. 435-466
    • Gentili, G.1    Vignozzi, I.2
  • 70
    • 70349224324 scopus 로고    scopus 로고
    • Rigidity for regular functions over Hamilton and Cayley numbers and a boundary Schwarz Lemma
    • G. Gentili, F. Vlacci, Rigidity for regular functions over Hamilton and Cayley numbers and a boundary Schwarz Lemma. Indag. Math. (N.S.) 19(4), 535–545 (2008)
    • (2008) Indag. Math. (N.S.) , vol.19 , Issue.4 , pp. 535-545
    • Gentili, G.1    Vlacci, F.2
  • 71
    • 84923785876 scopus 로고    scopus 로고
    • On fixed points of regular Möbius transformations over quaternions
    • vol., American Mathematical Society, Providence, ), pp
    • G. Gentili, F. Vlacci, On fixed points of regular Möbius transformations over quaternions, in Complex Analysis and Dynamical Systems IV. Part1. Contemporary Mathematics, vol. 553 (American Mathematical Society, Providence, 2011), pp. 75–82
    • (2011) Complex Analysis and Dynamical Systems IV. Part1. Contemporary Mathematics , vol.553 , pp. 75-82
    • Gentili, G.1    Vlacci, F.2
  • 72
    • 78149499649 scopus 로고    scopus 로고
    • Slice regular functions on real alternative algebras
    • R. Ghiloni, A. Perotti, Slice regular functions on real alternative algebras. Adv. Math. 226(2), 1662–1691 (2011)
    • (2011) Adv. Math. , vol.226 , Issue.2 , pp. 1662-1691
    • Ghiloni, R.1    Perotti, A.2
  • 73
    • 80051670116 scopus 로고    scopus 로고
    • Zeros of regular functions of quaternionic and octonionic variable: A division lemma and the camshaft effect
    • R. Ghiloni, A. Perotti, Zeros of regular functions of quaternionic and octonionic variable: A division lemma and the camshaft effect. Ann. Mat. Pura Appl. (4) 190(3), 539–551 (2011)
    • (2011) Ann. Mat. Pura Appl. (4) , vol.190 , Issue.3 , pp. 539-551
    • Ghiloni, R.1    Perotti, A.2
  • 74
    • 84886379693 scopus 로고    scopus 로고
    • Volume Cauchy formulas for slice functions on real associative *-algebras
    • to appear
    • R. Ghiloni, A. Perotti, Volume Cauchy formulas for slice functions on real associative *-algebras. Complex Var. Elliptic Equat. (to appear). doi:10.1080/17476933.2012.709851
    • Complex Var. Elliptic Equat.
    • Ghiloni, R.1    Perotti, A.2
  • 77
    • 84878646282 scopus 로고    scopus 로고
    • On the development of Bohr’s phenomenon in the context of quaternionic analysis and related problems
    • (Ho Chi Minh City University of Education Press, Ho Chi Minh City, ), pp
    • K. Gürlebeck, J. Morais, On the development of Bohr’s phenomenon in the context of quaternionic analysis and related problems, in Algebraic Structures in Partial Differential Equations Related to Complex and Clifford Analysis (Ho Chi Minh City University of Education Press, Ho Chi Minh City, 2010), pp. 9–24
    • (2010) Algebraic Structures in Partial Differential Equations Related to Complex and Clifford Analysis , pp. 9-24
    • Gürlebeck, K.1    Morais, J.2
  • 78
  • 79
    • 70450148746 scopus 로고    scopus 로고
    • Bohr type theorems for monogenic power series
    • K. Gürlebeck, J.P. Morais, Bohr type theorems for monogenic power series. Comput. Meth. Funct. Theor. 9(2), 633–651 (2009)
    • (2009) Comput. Meth. Funct. Theor. , vol.9 , Issue.2 , pp. 633-651
    • Gürlebeck, K.1    Morais, J.P.2
  • 81
    • 21244446348 scopus 로고
    • Die Winkelderivierte und das Poisson-Stieltjes-Integral
    • A. Herzig, Die Winkelderivierte und das Poisson-Stieltjes-Integral. Math. Z. 46, 129–156 (1940)
    • (1940) Math. Z. , vol.46 , pp. 129-156
    • Herzig, A.1
  • 82
    • 0030150764 scopus 로고    scopus 로고
    • The Riesz-Clifford functional calculus for non-commuting operators and quantum field theory
    • V.V. Kisil, E. Ramírez de Arellano, The Riesz-Clifford functional calculus for non-commuting operators and quantum field theory. Math. Meth. Appl. Sci. 19(8), 593–605 (1996)
    • (1996) Math. Meth. Appl. Sci. , vol.19 , Issue.8 , pp. 593-605
    • Kisil, V.V.1    Ramírez de Arellano, E.2
  • 83
    • 0001082430 scopus 로고    scopus 로고
    • Integral representations for spatial models of mathematical physics
    • vol., Longman, Harlow
    • V.V. Kravchenko, M.V. Shapiro, Integral representations for spatial models of mathematical physics. Pitman Research Notes in Mathematics Series, vol. 351 (Longman, Harlow, 1996)
    • (1996) Pitman Research Notes in Mathematics Series , vol.351
    • Kravchenko, V.V.1    Shapiro, M.V.2
  • 90
    • 0004248071 scopus 로고    scopus 로고
    • Distribution of zeros of entire functions
    • revised edn. (American Mathematical Society, Providence, 1980), (Translated from the Russian by R.P. Boas et al.)
    • B.J. Levin, Distribution of zeros of entire functions. Translations of Mathematical Monographs, vol. 5, revised edn. (American Mathematical Society, Providence, 1980), pp. 47–51 (Translated from the Russian by R.P. Boas et al.)
    • Translations of Mathematical Monographs , vol.5 , pp. 47-51
    • Levin, B.J.1
  • 91
    • 0041333025 scopus 로고    scopus 로고
    • The Cauchy integral formulas on the octonions
    • X. Li, L. Peng, The Cauchy integral formulas on the octonions. Bull. Belg. Math. Soc. Simon Stevin 9(1), 47–64 (2002)
    • (2002) Bull. Belg. Math. Soc. Simon Stevin , vol.9 , Issue.1 , pp. 47-64
    • Li, X.1    Peng, L.2
  • 93
    • 84956483131 scopus 로고    scopus 로고
    • On the hyperderivatives of Dirac-hyperholomorphic functions of Clifford analysis
    • ed. by J.A. Ball, R.E. Curto, S.M. Grudsky, J.W. Helton, R. Quiroga-Barranco, N.L. Vasilevski. Operator Theory: Advances and Applications, vol., Springer, Basel, ), pp
    • M. Luna-Elizarrarás, M. Macías-Cedeño, M. Shapiro, On the hyperderivatives of Dirac-hyperholomorphic functions of Clifford analysis, in Recent Progress in Operator Theory and Its Applications, ed. by J.A. Ball, R.E. Curto, S.M. Grudsky, J.W. Helton, R. Quiroga-Barranco, N.L. Vasilevski. Operator Theory: Advances and Applications, vol. 220 (Springer, Basel, 2012), pp. 179–195
    • (2012) Recent Progress in Operator Theory and Its Applications , vol.220 , pp. 179-195
    • Luna-Elizarrarás, M.1    Macías-Cedeño, M.2    Shapiro, M.3
  • 94
    • 84961375148 scopus 로고    scopus 로고
    • Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals
    • in Hypercomplex Analysis, ed., I. Sabadini, M.V. Shapiro, F. Sommen, Birkhäuser, Basel, ), pp
    • M.E. Luna-Elizarrarás, M.A. Macías-Cedeño, M. Shapiro, Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals, in Hypercomplex Analysis, ed. by I. Sabadini, M.V. Shapiro, F. Sommen. Trends in Mathematics (Birkhäuser, Basel, 2009), pp. 221–234
    • (2009) Trends in Mathematics , pp. 221-234
    • Luna-Elizarrarás, M.E.1    Macías-Cedeño, M.A.2    Shapiro, M.3
  • 95
    • 84961364571 scopus 로고    scopus 로고
    • On the hyperderivatives of Moisil– Théodoresco hyperholomorphic functions
    • ed. by I. Sabadini, F. Sommen. Trends in Mathematics (Birkhäuser, Basel, 2011)
    • M.E. Luna-Elizarrarás, M.A. Macías-Cedeño, M. Shapiro, On the hyperderivatives of Moisil– Théodoresco hyperholomorphic functions, in Hypercomplex Analysis and Applications, ed. by I. Sabadini, F. Sommen. Trends in Mathematics (Birkhäuser, Basel, 2011), pp. 181–193
    • Hypercomplex Analysis and Applications , pp. 181-193
    • Luna-Elizarrarás, M.E.1    Macías-Cedeño, M.A.2    Shapiro, M.3
  • 96
    • 81955161818 scopus 로고    scopus 로고
    • A survey on the (Hyper-) derivatives in complex, quaternionic and Clifford analysis
    • M.E. Luna-Elizarrarás, M. Shapiro, A survey on the (hyper-) derivatives in complex, quaternionic and Clifford analysis. Milan J. Math. 79(2), 521–542 (2011)
    • (2011) Milan J. Math. , vol.79 , Issue.2 , pp. 521-542
    • Luna-Elizarrarás, M.E.1    Shapiro, M.2
  • 98
    • 0037970073 scopus 로고    scopus 로고
    • A new rigidity result for holomorphic maps
    • S. Migliorini, F. Vlacci, A new rigidity result for holomorphic maps. Indag. Math. (N.S.) 13(4), 537–549 (2002)
    • (2002) Indag. Math. (N.S.) , vol.13 , Issue.4 , pp. 537-549
    • Migliorini, S.1    Vlacci, F.2
  • 99
    • 84985376331 scopus 로고
    • Differentiation of the Martinelli-Bochner integrals and the notion of hyperderivability
    • I.M. Mitelman, M.V. Shapiro, Differentiation of the Martinelli-Bochner integrals and the notion of hyperderivability. Math. Nachr. 172, 211–238 (1995)
    • (1995) Math. Nachr. , vol.172 , pp. 211-238
    • Mitelman, I.M.1    Shapiro, M.V.2
  • 100
    • 0000003348 scopus 로고
    • Equations in quaternions
    • I. Niven, Equations in quaternions. Am. Math. Mon. 48, 654–661 (1941)
    • (1941) Am. Math. Mon , vol.48 , pp. 654-661
    • Niven, I.1
  • 102
    • 15844411904 scopus 로고    scopus 로고
    • Algebraic tools for the study of quaternionic behavioral systems
    • R. Pereira, P. Rocha, P. Vettori, Algebraic tools for the study of quaternionic behavioral systems. Linear Algebra Appl. 400, 121–140 (2005)
    • (2005) Linear Algebra Appl , vol.400 , pp. 121-140
    • Pereira, R.1    Rocha, P.2    Vettori, P.3
  • 103
    • 33644942141 scopus 로고    scopus 로고
    • Stability of quaternionic linear systems
    • R. Pereira, P. Vettori, Stability of quaternionic linear systems. IEEE Trans. Automat. Contr. 51(3), 518–523 (2006)
    • (2006) IEEE Trans. Automat. Contr. , vol.51 , Issue.3 , pp. 518-523
    • Pereira, R.1    Vettori, P.2
  • 105
    • 24844446475 scopus 로고
    • Sur une extension d’un théorème classique de la théorie des fonctions
    • E. Phragmén, Sur une extension d’un théorème classique de la théorie des fonctions. Acta Math. 28(1), 351–368 (1904)
    • (1904) Acta Math , vol.28 , Issue.1 , pp. 351-368
    • Phragmén, E.1
  • 106
    • 4243252777 scopus 로고
    • Sur une extension d’un principe classique de l’analyse et sur quelques propriétés des fonctions monogènes dans le voisinage d’un point singulier
    • E. Phragmén, E. Lindelöf, Sur une extension d’un principe classique de l’analyse et sur quelques propriétés des fonctions monogènes dans le voisinage d’un point singulier. Acta Math. 31(1), 381–406 (1908)
    • (1908) Acta Math , vol.31 , Issue.1 , pp. 381-406
    • Phragmén, E.1    Lindelöf, E.2
  • 107
    • 34548181323 scopus 로고    scopus 로고
    • On the structure of the set of zeros of quaternionic polynomials
    • A. Pogorui, M. Shapiro, On the structure of the set of zeros of quaternionic polynomials. Complex Var. Theor. Appl. 49(6), 379–389 (2004)
    • (2004) Complex Var. Theor. Appl. , vol.49 , Issue.6 , pp. 379-389
    • Pogorui, A.1    Shapiro, M.2
  • 108
    • 0012187543 scopus 로고
    • Theory of complex functions
    • vol., Readings in Mathematics (Springer, New York
    • R. Remmert, Theory of complex functions. Graduate Texts in Mathematics, vol. 122. Readings in Mathematics (Springer, New York, 1991)
    • (1991) Graduate Texts in Mathematics , vol.122
    • Remmert, R.1
  • 111
    • 0001101281 scopus 로고
    • Cells of harmonicity and generalized Cauchy integral formulae
    • J. Ryan, Cells of harmonicity and generalized Cauchy integral formulae. Proc. Lond. Math. Soc. (3) 60(2), 295–318 (1990)
    • (1990) Proc. Lond. Math. Soc. (3) , vol.60 , Issue.2 , pp. 295-318
    • Ryan, J.1
  • 112
    • 84972038116 scopus 로고
    • Complex Clifford analysis and domains of holomorphy
    • J. Ryan, Complex Clifford analysis and domains of holomorphy. J. Aust. Math. Soc. Ser. A 48(3), 413–433 (1990)
    • (1990) J. Aust. Math. Soc. Ser. A , vol.48 , Issue.3 , pp. 413-433
    • Ryan, J.1
  • 113
    • 77952644506 scopus 로고    scopus 로고
    • First order differential operators in real dimension eight
    • I. Sabadini, D.C. Struppa, First order differential operators in real dimension eight. Complex Var. Theor. Appl. 47(10), 953–968 (2002)
    • (2002) Complex Var. Theor. Appl. , vol.47 , Issue.10 , pp. 953-968
    • Sabadini, I.1    Struppa, D.C.2
  • 115
    • 0011469690 scopus 로고    scopus 로고
    • Zeros of quaternion polynomials
    • R. Serôdio, L.-S. Siu, Zeros of quaternion polynomials. Appl. Math. Lett. 14(2), 237–239 (2001)
    • (2001) Appl. Math. Lett. , vol.14 , Issue.2 , pp. 237-239
    • Serôdio, R.1    Siu, L.-S.2
  • 116
    • 0039143440 scopus 로고
    • Quaternionic-hyperholomorphic functions, singular integral operators and boundary value problems. I.-hyperholomorphic function theory
    • M.V. Shapiro, N.L. Vasilevski, Quaternionic-hyperholomorphic functions, singular integral operators and boundary value problems. I.-hyperholomorphic function theory. Complex Var. Theor. Appl. 27(1), 17–46 (1995)
    • (1995) Complex Var. Theor. Appl. , vol.27 , Issue.1 , pp. 17-46
    • Shapiro, M.V.1    Vasilevski, N.L.2
  • 117
    • 0002726228 scopus 로고
    • Some connections between Clifford analysis and complex analysis
    • F. Sommen, Some connections between Clifford analysis and complex analysis. Complex Var. Theor. Appl. 1(1), 97–118 (1982/1983)
    • (1982) Complex Var. Theor. Appl. , vol.1 , Issue.1 , pp. 97-118
    • Sommen, F.1
  • 119
    • 75249106341 scopus 로고    scopus 로고
    • Poles of regular quaternionic functions
    • C. Stoppato, Poles of regular quaternionic functions. Complex Var. Elliptic Equat. 54(11), 1001–1018 (2009)
    • (2009) Complex Var. Elliptic Equat. , vol.54 , Issue.11 , pp. 1001-1018
    • Stoppato, C.1
  • 121
    • 79952449747 scopus 로고    scopus 로고
    • Regular Moebius transformations of the space of quaternions
    • C. Stoppato, Regular Moebius transformations of the space of quaternions. Ann. Global Anal. Geom. 39(4) 387–401 (2011)
    • (2011) Ann. Global Anal. Geom. , vol.39 , Issue.4 , pp. 387-401
    • Stoppato, C.1
  • 122
    • 84864817223 scopus 로고    scopus 로고
    • A new series expansion for slice regular functions
    • C. Stoppato, A new series expansion for slice regular functions. Adv. Math. 231(3–4), 1401– 1416 (2012)
    • (2012) Adv. Math. , vol.231 , Issue.3-4 , pp. 1401-1416
    • Stoppato, C.1
  • 123
    • 84863559558 scopus 로고    scopus 로고
    • Singularities of slice regular functions
    • C. Stoppato, Singularities of slice regular functions. Math. Nachr. 285(10), 1274–1293 (2012)
    • (2012) Math. Nachr. , vol.285 , Issue.10 , pp. 1274-1293
    • Stoppato, C.1
  • 127
    • 79953668737 scopus 로고    scopus 로고
    • The argument principle for quaternionic slice regular functions
    • F. Vlacci, The argument principle for quaternionic slice regular functions. Mich. Math. J. 60(1), 67–77 (2011)
    • (2011) Mich. Math. J. , vol.60 , Issue.1 , pp. 67-77
    • Vlacci, F.1
  • 129
  • 130
    • 0000208756 scopus 로고
    • Harmonic morphisms and Hermitian structures on Einstein 4-manifolds
    • J.C. Wood, Harmonic morphisms and Hermitian structures on Einstein 4-manifolds. Int. J. Math. 3(3), 415–439 (1992)
    • (1992) Int. J. Math. , vol.3 , Issue.3 , pp. 415-439
    • Wood, J.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.