Envelopes of holomorphy and extension of functions of bounded type

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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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Autores principales:	Carando, D., Muro, S.
Formato:	Artículo publishedVersion
Lenguaje:	Inglés
Publicado:	2012
Materias:	Envelope of holomorphy Holomorphic functions of bounded type Riemann domains
Acceso en línea:	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	paperaa:paper_00018708_v229_n3_p2098_Carando
record_format	dspace
spelling	paperaa:paper_00018708_v229_n3_p2098_Carando2023-06-12T16:39:29Z Envelopes of holomorphy and extension of functions of bounded type Adv. Math. 2012;229(3):2098-2121 Carando, D. Muro, S. 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 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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)
language	Inglés
orig_language_str_mv	eng
topic	Envelope of holomorphy Holomorphic functions of bounded type Riemann domains
spellingShingle	Envelope of holomorphy Holomorphic functions of bounded type Riemann domains Carando, D. Muro, S. 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.
format	Artículo Artículo publishedVersion
author	Carando, D. Muro, S.
author_facet	Carando, D. Muro, S.
author_sort	Carando, D.
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	http://hdl.handle.net/20.500.12110/paper_00018708_v229_n3_p2098_Carando
work_keys_str_mv	AT carandod envelopesofholomorphyandextensionoffunctionsofboundedtype AT muros envelopesofholomorphyandextensionoffunctionsofboundedtype
_version_	1769810201049825280

Envelopes of holomorphy and extension of functions of bounded type

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