Envelopes of holomorphy and extension of functions of bounded type

We study the extension of holomorphic functions of bounded type defined on an open subset of a Banach space to larger domains. For this, we first characterize the envelope of holomorphy of a Riemann domain over a Banach space, with respect to the algebra of bounded type holomorphic functions, in ter...

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Detalles Bibliográficos
Autores principales: Carando, Daniel German, Muro, Santiago
Publicado: 2012
Materias:
Envelope of holomorphy
Holomorphic functions of bounded type
Riemann domains
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v229_n3_p2098_Carando
http://hdl.handle.net/20.500.12110/paper_00018708_v229_n3_p2098_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00018708_v229_n3_p2098_Carando
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spelling paper:paper_00018708_v229_n3_p2098_Carando2023-06-08T14:21:47Z Envelopes of holomorphy and extension of functions of bounded type Carando, Daniel German Muro, Santiago Envelope of holomorphy Holomorphic functions of bounded type Riemann domains We study the extension of holomorphic functions of bounded type defined on an open subset of a Banach space to larger domains. For this, we first characterize the envelope of holomorphy of a Riemann domain over a Banach space, with respect to the algebra of bounded type holomorphic functions, in terms of the spectrum of the algebra. We then give a simple description of the envelopes of balanced open sets and relate the concepts of domain of holomorphy and polynomial convexity. We show that for bounded balanced sets, extensions to the envelope are always of bounded type, and that this does not necessarily hold for unbounded sets, answering a question posed by Hirschowitz in 1972. We also consider extensions to open subsets of the bidual, present some Banach-Stone type results and show some properties of the spectrum when the domain is the unit ball of ℓ p. © 2011 Elsevier Inc. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Muro, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v229_n3_p2098_Carando http://hdl.handle.net/20.500.12110/paper_00018708_v229_n3_p2098_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Envelope of holomorphy
Holomorphic functions of bounded type
Riemann domains
spellingShingle Envelope of holomorphy
Holomorphic functions of bounded type
Riemann domains
Carando, Daniel German
Muro, Santiago
Envelopes of holomorphy and extension of functions of bounded type
topic_facet Envelope of holomorphy
Holomorphic functions of bounded type
Riemann domains
description We study the extension of holomorphic functions of bounded type defined on an open subset of a Banach space to larger domains. For this, we first characterize the envelope of holomorphy of a Riemann domain over a Banach space, with respect to the algebra of bounded type holomorphic functions, in terms of the spectrum of the algebra. We then give a simple description of the envelopes of balanced open sets and relate the concepts of domain of holomorphy and polynomial convexity. We show that for bounded balanced sets, extensions to the envelope are always of bounded type, and that this does not necessarily hold for unbounded sets, answering a question posed by Hirschowitz in 1972. We also consider extensions to open subsets of the bidual, present some Banach-Stone type results and show some properties of the spectrum when the domain is the unit ball of ℓ p. © 2011 Elsevier Inc.
author Carando, Daniel German
Muro, Santiago
author_facet Carando, Daniel German
Muro, Santiago
author_sort Carando, Daniel German
title Envelopes of holomorphy and extension of functions of bounded type
title_short Envelopes of holomorphy and extension of functions of bounded type
title_full Envelopes of holomorphy and extension of functions of bounded type
title_fullStr Envelopes of holomorphy and extension of functions of bounded type
title_full_unstemmed Envelopes of holomorphy and extension of functions of bounded type
title_sort envelopes of holomorphy and extension of functions of bounded type
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v229_n3_p2098_Carando
http://hdl.handle.net/20.500.12110/paper_00018708_v229_n3_p2098_Carando
work_keys_str_mv AT carandodanielgerman envelopesofholomorphyandextensionoffunctionsofboundedtype
AT murosantiago envelopesofholomorphyandextensionoffunctionsofboundedtype
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