Duality theorems for slice hyperholomorphic functions

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 645, 2010, Pages 85-104

  Colombo, Fabrizio ^a   Sabadini, Irene ^a   Struppa, Daniele C ^b  

^a POLITECNICO DI MILANO   (Italy)

^b CHAPMAN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954365658     PISSN: 00754102     EISSN: 00754102     Source Type: Journal    
DOI: 10.1515/CRELLE.2010.060     Document Type: Article

References (18)

1. F. Brackx, R. Delanghe, F. Sommen, Clifford Analysis, Pitman Res. Notes Math. 76 (1982).
2. F. Colombo, I. Sabadini, A structure formula for slice monogenic functions and some of its consequences, Hypercomplex Analysis, Trends in Mathematics, Birkhäuser (2009), 101-114.
3. F. Colombo, I. Sabadini, The Cauchy formula with s-monogenic kernel and a functional calculus for non-commuting operators, preprint 2008.
4. F. Colombo, I. Sabadini, F. Sommen, D. C. Struppa, Analysis of Dirac systems and computational algebra, Progr. Math. Phys. 39, Birkhäuser, Boston 2004.
5. F. Colombo, I. Sabadini, D. C. Struppa, A new functional calculus for noncommuting operators, J. Funct. Anal. 254 (2008), 2255-2274.
6. F. Colombo, I. Sabadini, D. C. Struppa, Slice monogenic functions, Israel J. Math. 171 (2009), 385-403.
7. F. Colombo, I. Sabadini, D. C. Struppa, Extension properties for slice monogenic functions, Israel J. Math. 177 (2010), 369-389.
8. C. G. Cullen, An integral theorem for analytic intrinsic functions on quaternions, Duke Math. J. 32 (1965), 139-148.
9. A. Fabiano, G. Gentili, D. C. Struppa, Sheaves of quaternionic hyperfunctions and microfunctions, Compl. Variab. Th. Appl. 24 (1994), 161-184.
10. G. Gentili, D. C. Struppa, A new theory of regular functions of a quaternionic variable, Adv. Math. 216 (2007), 279-301.
11. A. Grothendieck, Sur certain espaces de fonctions holomorphes, I, II, J. reine angew. Math. 192 (1953), 35-64, 77-95.
12. L. Hörmander, The Analysis of Linear Partial Differential Operators, I, Springer Verlag, Berlin-Heidelberg 1983.
13. A. Kaneko, Introduction to Hyperfunctions, Kluwer, 1994.
14. G. Kato, D. C. Struppa, Fundamentals of Algebraic Microlocal Analysis, Marcel Dekker, New York 1999.
15. G. Köthe, Dualität in der Funktionentheorie, J. reine angew. Math. 191 (1953), 30-49.
16. A. Martineau, Indicatrices des fonctionelles analytiques et transfomée de Laplace, in: Oeuvres de André Martineau, Éditions du Centre National de la Recherche Scientifique (CNRS), Paris (1977), 595-608.
17. I. Sabadini, D. C. Struppa, Topologies on quaternionic hyperfunctions and duality theorems, Complex Var. Th. Appl. 30 (1996), 19-34.
18. F. Sommen, Microfunctions with values in a Clifford algebra, II, Sci. Papers College Arts Sci. Univ. Tokyo 36 (1986), 15-37.