Hyperholomorphic bergman spaces and bergman operators associated with domains in ℂ2

José Óscar González-Cervantes; Michael Shapiro

doi:10.1007/s11785-008-0057-y

Hyperholomorphic bergman spaces and bergman operators associated with domains in ℂ²

José Óscar González-Cervantes, Michael Shapiro

Escuela Superior de Física y Matemáticas (ESFM)

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The work deals with a version of quaternionic analysis adapted in such a way that the set of arising hyperholomorphic functions includes, as a proper subset, all holomorphic mappings. There are considered, for the theory of the corresponding Bergman spaces and Bergman operators, both classic, commonly treated aspects and more specific ones, in particular, conformally invariant or covariant character of certain objects; a description of an algebra generated by the Bergman projection together with a criterion ensuring the Fredholmness of elements of the algebra; relations with the usual holomorphic mappings theory in two complex variables are demonstrated as well.

Original language	English
Pages (from-to)	361-382
Number of pages	22
Journal	Complex Analysis and Operator Theory
Volume	2
Issue number	2
DOIs	https://doi.org/10.1007/s11785-008-0057-y
State	Published - May 2008

Keywords

Bergman kernels
Bergman operators
Bergman spaces
Quaternionic Möbius transformations
Quaternionic analysis

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10.1007/s11785-008-0057-y

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title = "Hyperholomorphic bergman spaces and bergman operators associated with domains in ℂ2",

abstract = "The work deals with a version of quaternionic analysis adapted in such a way that the set of arising hyperholomorphic functions includes, as a proper subset, all holomorphic mappings. There are considered, for the theory of the corresponding Bergman spaces and Bergman operators, both classic, commonly treated aspects and more specific ones, in particular, conformally invariant or covariant character of certain objects; a description of an algebra generated by the Bergman projection together with a criterion ensuring the Fredholmness of elements of the algebra; relations with the usual holomorphic mappings theory in two complex variables are demonstrated as well.",

keywords = "Bergman kernels, Bergman operators, Bergman spaces, Quaternionic M{\"o}bius transformations, Quaternionic analysis",

author = "Gonz{\'a}lez-Cervantes, {Jos{\'e} {\'O}scar} and Michael Shapiro",

note = "Funding Information: The first-named author was partially supported by CONACYT and by IPN as Doctoral scholarship and PIFI scholarship recipient.The second-named author was partially supported by CONA-CYT projects as well as by IPN in the framework of COFAA and SIP programs.",

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T1 - Hyperholomorphic bergman spaces and bergman operators associated with domains in ℂ2

AU - González-Cervantes, José Óscar

AU - Shapiro, Michael

N1 - Funding Information: The first-named author was partially supported by CONACYT and by IPN as Doctoral scholarship and PIFI scholarship recipient.The second-named author was partially supported by CONA-CYT projects as well as by IPN in the framework of COFAA and SIP programs.

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N2 - The work deals with a version of quaternionic analysis adapted in such a way that the set of arising hyperholomorphic functions includes, as a proper subset, all holomorphic mappings. There are considered, for the theory of the corresponding Bergman spaces and Bergman operators, both classic, commonly treated aspects and more specific ones, in particular, conformally invariant or covariant character of certain objects; a description of an algebra generated by the Bergman projection together with a criterion ensuring the Fredholmness of elements of the algebra; relations with the usual holomorphic mappings theory in two complex variables are demonstrated as well.

AB - The work deals with a version of quaternionic analysis adapted in such a way that the set of arising hyperholomorphic functions includes, as a proper subset, all holomorphic mappings. There are considered, for the theory of the corresponding Bergman spaces and Bergman operators, both classic, commonly treated aspects and more specific ones, in particular, conformally invariant or covariant character of certain objects; a description of an algebra generated by the Bergman projection together with a criterion ensuring the Fredholmness of elements of the algebra; relations with the usual holomorphic mappings theory in two complex variables are demonstrated as well.

KW - Bergman kernels

KW - Bergman operators

KW - Bergman spaces

KW - Quaternionic Möbius transformations

KW - Quaternionic analysis

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DO - 10.1007/s11785-008-0057-y

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EP - 382

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

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ER -

Hyperholomorphic bergman spaces and bergman operators associated with domains in ℂ²

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Keywords

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