메뉴 건너뛰기




Volumn 176, Issue 3, 2012, Pages 1783-1826

Operator monotone functions and Löwner functions of several variables

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84870684556     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2012.176.3.7     Document Type: Article
Times cited : (69)

References (38)
  • 1
    • 0032410608 scopus 로고    scopus 로고
    • The Julia-Wolff-Carathéodory theorem in polydisks
    • MR 1631670. Zbl 0912.32005
    • M. Abate, The Julia-Wolff-Carathéodory theorem in polydisks, J. Anal. Math. 74 (1998), 275-306. MR 1631670. Zbl 0912.32005. http://dx.doi.org/10.1007/BF02819453.
    • (1998) J. Anal. Math. , vol.74 , pp. 275-306
    • Abate, M.1
  • 2
    • 0001876004 scopus 로고
    • On the representation of certain holomorphic functions defined on a polydisc
    • Birkhäuser, Basel, MR 1207393. Zbl 0733.32002
    • J. Agler, On the representation of certain holomorphic functions defined on a polydisc, in Topics in Operator Theory: Ernst D. Hellinger Memorial Volume, Oper. Theory Adv. Appl. 48, Birkhäuser, Basel, 1990, pp. 47-66. MR 1207393. Zbl 0733.32002.
    • (1990) Topics in Operator Theory: Ernst D. Hellinger Memorial Volume, Oper. Theory Adv. Appl. , vol.48 , pp. 47-66
    • Agler, J.1
  • 3
    • 0012851645 scopus 로고    scopus 로고
    • Pick Interpolation and Hilbert Function Spaces, Grad. Studies in Math.
    • Providence, RI, 2002. MR 1882259. Zbl 1010.47001
    • J. Agler and J. E. McCarthy, Pick Interpolation and Hilbert Function Spaces, Grad. Studies in Math. no. 44, Amer. Math. Soc., Providence, RI, 2002. MR 1882259. Zbl 1010.47001.
    • Amer. Math. Soc. , vol.44
    • Agler, J.1    Mccarthy, J.E.2
  • 4
    • 84856210812 scopus 로고    scopus 로고
    • A Carathéodory theorem for the bidisk via Hilbert space methods
    • MR 2885589. Zbl 06008815
    • J. Agler, J. E. McCarthy, and N. Young, A Carathéodory theorem for the bidisk via Hilbert space methods, Math. Ann. 352 (2012), 581-624. MR 2885589. Zbl 06008815. http://dx.doi.org/10.1007/s00208-011-0650-7.
    • (2012) Math. Ann. , vol.352 , pp. 581-624
    • Agler, J.1    Mccarthy, J.E.2    Young, N.3
  • 5
    • 0011695218 scopus 로고
    • General Topology. I
    • Springer-Verlag, New York, MR 1077251. Zbl 0778.00007
    • A. Arkhangel'skii and L. Pontryagin (eds.), General Topology. I, Encycl. Math. Sci. 17, Springer-Verlag, New York, 1990. MR 1077251. Zbl 0778.00007.
    • (1990) Encycl. Math. Sci. , vol.17
    • Arkhangel'skii, A.1    Pontryagin, L.2
  • 6
    • 0037107106 scopus 로고    scopus 로고
    • A tangential interpolation problem on the distinguished boundary of the polydisk for the Schur-Agler class
    • MR 1932492. Zbl 1015.47004
    • J. A. Ball and V. Bolotnikov, A tangential interpolation problem on the distinguished boundary of the polydisk for the Schur-Agler class, J. Math. Anal. Appl. 273 (2002), 328-348. MR 1932492. Zbl 1015.47004. http://dx.doi.org/10.101/S0022-247X(02)00226-3.
    • (2002) J. Math. Anal. Appl. , vol.273 , pp. 328-348
    • Ball, J.A.1    Bolotnikov, V.2
  • 7
    • 79751526543 scopus 로고    scopus 로고
    • Canonical de Branges-Rovnyak model transfer-function realization for multivariable Schur-class functions, in Hilbert Spaces of Analytic Functions, CRM Proc. Lecture Notes 51
    • MR 2648864. Zbl 1210.47041
    • J. A. Ball, Canonical de Branges-Rovnyak model transfer-function realization for multivariable Schur-class functions, in Hilbert Spaces of Analytic Functions, CRM Proc. Lecture Notes 51, Amer. Math. Soc., Providence, RI, 2010, pp. 1-39. MR 2648864. Zbl 1210.47041.
    • (2010) Amer. Math. Soc., Providence, RI , pp. 1-39
    • Ball, J.A.1
  • 8
    • 23644432815 scopus 로고    scopus 로고
    • Scattering systems with several evolutions and multidimensional input/state/output systems
    • MR 2184571. Zbl 1092.47006
    • J. A. Ball, C. Sadosky, and V. Vinnikov, Scattering systems with several evolutions and multidimensional input/state/output systems, Integral Equations Operator Theory 52 (2005), 323-393. MR 2184571. Zbl 1092.47006. http://dx.doi.org/10.1007/s00020-005-1351-y.
    • (2005) Integral Equations Operator Theory , vol.52 , pp. 323-393
    • Ball, J.A.1    Sadosky, C.2    Vinnikov, V.3
  • 9
    • 0001858717 scopus 로고    scopus 로고
    • Unitary colligations, reproducing kernel Hilbert spaces, and Nevanlinna-Pick interpolation in several variables
    • MR 1637941. Zbl 0914.47020
    • J. A. Ball and T. T. Trent, Unitary colligations, reproducing kernel Hilbert spaces, and Nevanlinna-Pick interpolation in several variables, J. Funct. Anal. 157 (1998), 1-61. MR 1637941. Zbl 0914.47020. http://dx.doi.org/10.1006/jfan.1998.3278.
    • (1998) J. Funct. Anal. , vol.157 , pp. 1-61
    • Ball, J.A.1    Trent, T.T.2
  • 10
    • 84872438588 scopus 로고    scopus 로고
    • Differentiating matrix functions
    • K. Bickel, Differentiating matrix functions, Operators and Matrices 7 (2013), 71-90. http://dx.doi.org/10.7153/oam-07-03.
    • (2013) Operators and Matrices , vol.7 , pp. 71-90
    • Bickel, K.1
  • 11
    • 84966256895 scopus 로고
    • Extensions of monotone operator functions
    • MR 0394271. Zbl 0308.47028
    • J. D. Chandler, Jr., Extensions of monotone operator functions, Proc. Amer. Math. Soc. 54 (1976), 221-224. MR 0394271. Zbl 0308.47028.
    • (1976) Proc. Amer. Math. Soc. , vol.54 , pp. 221-224
    • Chandler Jr., J.D.1
  • 12
    • 0348224117 scopus 로고    scopus 로고
    • Ando's theorem and sums of squares
    • MR 1736979. Zbl 0945.47010
    • B. J. Cole and J. Wermer, Ando's theorem and sums of squares, Indiana Univ. Math. J. 48 (1999), 767-791. MR 1736979. Zbl 0945.47010. http://dx.doi.org/10.1512/iumj.1999.48.1716.
    • (1999) Indiana Univ. Math. J. , vol.48 , pp. 767-791
    • Cole, B.J.1    Wermer, J.2
  • 13
    • 0041969413 scopus 로고
    • von Neumann's inequality for Hilbert space operators
    • MR 0365179. Zbl 0301. 47007
    • M. J. Crabb and A. M. Davie, von Neumann's inequality for Hilbert space operators, Bull. London Math. Soc. 7 (1975), 49-50. MR 0365179. Zbl 0301. 47007. http://dx.doi.org/10.1112/blms/7.1.49.
    • (1975) Bull. London Math. Soc. , vol.7 , pp. 49-50
    • Crabb, M.J.1    Davie, A.M.2
  • 14
    • 0038245757 scopus 로고
    • Monotone Matrix Functions and Analytic Continuation
    • Springer-Verlag, New York, MR 0486556. Zbl 0278.30004
    • W. F. Donoghue, Jr., Monotone Matrix Functions and Analytic Continuation, Grundlehren Math. Wissen. 207, Springer-Verlag, New York, 1974. MR 0486556. Zbl 0278.30004.
    • (1974) Grundlehren Math. Wissen. , vol.207
    • Donoghue Jr., W.F.1
  • 15
    • 0003639010 scopus 로고    scopus 로고
    • A Course in Robust Control Theory
    • Springer-Verlag, New York, Zbl 0939.93001
    • G. E. Dullerud and F. Paganini, A Course in Robust Control Theory, Texts Appl. Math. 36, Springer-Verlag, New York, 2000. Zbl 0939.93001.
    • (2000) Texts Appl. Math. , vol.36
    • Dullerud, G.E.1    Paganini, F.2
  • 16
    • 0037276848 scopus 로고    scopus 로고
    • Operator monotone functions of several variables
    • MR 1950646. Zbl 1035.47005
    • F. Hansen, Operator monotone functions of several variables, Math. Inequal. Appl. 6 (2003), 1-17. MR 1950646. Zbl 1035.47005. http://dx.doi.org/10.7153/mia-06-01.
    • (2003) Math. Inequal. Appl. , vol.6 , pp. 1-17
    • Hansen, F.1
  • 17
    • 0002163623 scopus 로고
    • Über potenzreihen mit positivem, reelem Teil in Einheitskreis
    • JFM 42.0438.02
    • G. Herglotz, Über potenzreihen mit positivem, reelem Teil in Einheitskreis, Leipz. Bericht 63 (1911), 501-511. JFM 42.0438.02.
    • (1911) Leipz. Bericht , vol.63 , pp. 501-511
    • Herglotz, G.1
  • 18
    • 0003952516 scopus 로고    scopus 로고
    • Topics in Matrix Analysis
    • Cambridge Univ. Press, Cambridge, 1991. MR 1091716. Zbl 0729.15001
    • R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge Univ. Press, Cambridge, 1991. MR 1091716. Zbl 0729.15001. http://dx.doi.org/10.1017/CBO9780511840371.
    • Horn, R.A.1    Johnson, C.R.2
  • 19
    • 0003205756 scopus 로고
    • Angular derivatives in polydiscs
    • MR 1291722. Zbl 0820.32001
    • F. Jafari, Angular derivatives in polydiscs, Indian J. Math. 35 (1993), 197-212. MR 1291722. Zbl 0820.32001.
    • (1993) Indian J. Math. , vol.35 , pp. 197-212
    • Jafari, F.1
  • 20
    • 3042717614 scopus 로고    scopus 로고
    • On the Bessmertnyi class of homogeneous positive holomorphic functions of several variables, in Current Trends in Operator Theory and its Applications
    • Birkhäuser, Basel, MR 2063756. Zbl 1077.47012
    • D. S. Kaliuzhnyi-Verbovetskyi, On the Bessmertnyi class of homogeneous positive holomorphic functions of several variables, in Current Trends in Operator Theory and its Applications, Oper. Theory Adv. Appl. 149, Birkhäuser, Basel, 2004, pp. 255-289. MR 2063756. Zbl 1077.47012.
    • (2004) Oper. Theory Adv. Appl. , vol.149 , pp. 255-289
    • Kaliuzhnyi-Verbovetskyi, D.S.1
  • 21
    • 79960832086 scopus 로고    scopus 로고
    • Polynomials with no zeros on the bidisk
    • MR 2657451. Zbl 1226.42019
    • G. Knese, Polynomials with no zeros on the bidisk, Anal. PDE 3 (2010), 109-149. MR 2657451. Zbl 1226.42019. http://dx.doi.org/10.2140/apde.2010.3.109.
    • (2010) Anal. PDE , vol.3 , pp. 109-149
    • Knese, G.1
  • 22
    • 79958699230 scopus 로고    scopus 로고
    • Rational inner functions in the Schur-Agler class of the polydisk
    • MR 2839446. Zbl 1219.47028
    • G. Knese, Rational inner functions in the Schur-Agler class of the polydisk, Publ. Mat. 55 (2011), 343-357. MR 2839446. Zbl 1219.47028. http://dx.doi.org/10.5565/PUBLMAT5521104.
    • (2011) Publ. Mat. , vol.55 , pp. 343-357
    • Knese, G.1
  • 23
    • 84968510909 scopus 로고
    • On some classes of analytic functions of several variables
    • MR 0136765. Zbl 0111.11501
    • A. Korányi, On some classes of analytic functions of several variables, Trans. Amer. Math. Soc. 101 (1961), 520-554. MR 0136765. Zbl 0111.11501.
    • (1961) Trans. Amer. Math. Soc. , vol.101 , pp. 520-554
    • Korányi, A.1
  • 24
    • 0141995399 scopus 로고    scopus 로고
    • Functional Analysis
    • Wiley-Interscience [John Wiley & Sons], New York, 2002. MR 1892228. Zbl 1009.47001
    • P. D. Lax, Functional Analysis, Pure Appl. Math., Wiley-Interscience [John Wiley & Sons], New York, 2002. MR 1892228. Zbl 1009.47001.
    • Pure Appl. Math.
    • Lax, P.D.1
  • 25
    • 34250967722 scopus 로고
    • Über monotone Matrixfunktionen
    • MR 1545446. Zbl 0008.11301
    • K. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216. MR 1545446. Zbl 0008.11301. http://dx.doi.org/10.1007/BF01170633.
    • (1934) Math. Z. , vol.38 , pp. 177-216
    • Löwner, K.1
  • 26
    • 0002997583 scopus 로고
    • Asymptotische Entwicklungen beschränkter Funktionen und das Stieltjessche Momentproblem
    • JFM 48.1226.02
    • R. Nevanlinna, Asymptotische Entwicklungen beschränkter Funktionen und das Stieltjessche Momentproblem, Ann. Acad. Sci. Fenn. Ser. A 18 (1922). JFM 48.1226.02.
    • (1922) Ann. Acad. Sci. Fenn. Ser. A , vol.18
    • Nevanlinna, R.1
  • 27
    • 0000211649 scopus 로고
    • Remarques sur le lemme de Schwarz
    • JFM 55.0768.01
    • R. Nevanlinna, Remarques sur le lemme de Schwarz, C.R. Acad. Sci. Paris 188 (1929), 1027-1029. JFM 55.0768.01.
    • (1929) C.R. Acad. Sci. Paris , vol.188 , pp. 1027-1029
    • Nevanlinna, R.1
  • 28
    • 0002081029 scopus 로고
    • Hankel operators in the theory of perturbations of unitary and selfadjoint operators
    • 96. MR 0800919. Zbl 0587.47016
    • V. V. Peller, Hankel operators in the theory of perturbations of unitary and selfadjoint operators, Funktsional. Anal. i Prilozhen. 19 (1985), 37-51, 96. MR 0800919. Zbl 0587.47016.
    • (1985) Funktsional. Anal. i Prilozhen. , vol.19 , pp. 37-51
    • Peller, V.V.1
  • 29
    • 84982312405 scopus 로고    scopus 로고
    • The behavior of functions of operators under perturbations, in A Glimpse at Hilbert Space Operators
    • Birkhäuser, Basel, MR 2743424. Zbl 05872305
    • V. V. Peller, The behavior of functions of operators under perturbations, in A Glimpse at Hilbert Space Operators, Oper. Theory Adv. Appl. 207, Birkhäuser, Basel, 2010, pp. 287-324. MR 2743424. Zbl 05872305. http://dx.doi.org/10.1007/978-3-0346-0347-816.
    • (2010) Oper. Theory Adv. Appl. , vol.207 , pp. 287-324
    • Peller, V.V.1
  • 30
    • 0013542530 scopus 로고
    • Sur certaines inégalités dans la théorie des fonctions avec quelques remarques sur les geometries non-euclidiennes
    • Zbl 0003.25907
    • M. Riesz, Sur certaines inégalités dans la théorie des fonctions avec quelques remarques sur les geometries non-euclidiennes, Fysiogr. Sällsk. Lund Forh. 1 (1931), 18-38. Zbl 0003.25907.
    • (1931) Fysiogr. Sällsk. Lund Forh. , vol.1 , pp. 18-38
    • Riesz, M.1
  • 31
    • 84968497796 scopus 로고
    • Restrictions of analytic functions. I
    • MR 0399924. Zbl 0304.300
    • M. Rosenblum and J. Rovnyak, Restrictions of analytic functions. I, Proc. Amer. Math. Soc. 48 (1975), 113-119. MR 0399924. Zbl 0304.300.
    • (1975) Proc. Amer. Math. Soc. , vol.48 , pp. 113-119
    • Rosenblum, M.1    Rovnyak, J.2
  • 32
    • 0004133896 scopus 로고
    • W. A. Benjamin, New York, MR 0255841. Zbl 0177.34101
    • W. Rudin, Function Theory in Polydiscs, W. A. Benjamin, New York, 1969. MR 0255841. Zbl 0177.34101.
    • (1969) Function Theory in Polydiscs
    • Rudin, W.1
  • 33
    • 0013251709 scopus 로고
    • Lectures on the Edge-of-the-Wedge Theorem
    • Providence, RI, MR 0310288. Zbl 0214.09001
    • W. Rudin, Lectures on the Edge-of-the-Wedge Theorem, Amer. Math. Soc., Providence, RI, 1971. MR 0310288. Zbl 0214.09001.
    • (1971) Amer. Math. Soc.
    • Rudin, W.1
  • 34
    • 0004116414 scopus 로고
    • McGraw-Hill Book Co., New York, MR 0924157. Zbl 0925.00005
    • W. Rudin, Real and Complex Analysis, third ed., McGraw-Hill Book Co., New York, 1987. MR 0924157. Zbl 0925.00005.
    • (1987) Real and Complex Analysis, third ed.
    • Rudin, W.1
  • 35
    • 0032411776 scopus 로고    scopus 로고
    • Nevanlinna-Pick interpolation with boundary data
    • MR 1607902. Zbl 0906.30031
    • D. Sarason, Nevanlinna-Pick interpolation with boundary data, Integral Equations Operator Theory 30 (1998), 231-250. MR 1607902. Zbl 0906.30031. http://dx.doi.org/10.1007/BF01238220.
    • (1998) Integral Equations Operator Theory , vol.30 , pp. 231-250
    • Sarason, D.1
  • 36
    • 0035342072 scopus 로고    scopus 로고
    • Monotone matrix functions of two variables
    • MR 1823518. Zbl 0990.15010
    • M. Singh and H. L. Vasudeva, Monotone matrix functions of two variables, Linear Algebra Appl. 328 (2001), 131-152. MR 1823518. Zbl 0990.15010. http://dx.doi.org/10.1016/S0024-3795(00)00308-6.
    • (2001) Linear Algebra Appl. , vol.328 , pp. 131-152
    • Singh, M.1    Vasudeva, H.L.2
  • 37
    • 0003235349 scopus 로고
    • Linear Transformations in Hilbert Space and their Applications to Analysis
    • Amer. Math. Soc., New York, MR 1451877. Zbl 0005.40003.
    • M. H. Stone, Linear Transformations in Hilbert Space and their Applications to Analysis, Amer. Math. Soc. Colloq. Publ. 15, Amer. Math. Soc., New York, 1932. MR 1451877. Zbl 0005.40003.
    • (1932) Amer. Math. Soc. Colloq. Publ. , vol.15
    • Stone, M.H.1
  • 38
    • 0002834910 scopus 로고
    • On an inequality of von Neumann and an application of the metric theory of tensor products to operators theory
    • MR 0355642. Zbl 0288.47006
    • N. T. Varopoulos, On an inequality of von Neumann and an application of the metric theory of tensor products to operators theory, J. Funct. Anal. 16 (1974), 83-100. MR 0355642. Zbl 0288.47006.
    • (1974) J. Funct. Anal. , vol.16 , pp. 83-100
    • Varopoulos, N.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.