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
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v229_n3_p2098_Carando_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

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spelling	I28-R145-paper_00018708_v229_n3_p2098_Carando_oai2024-08-16 Carando, D. Muro, S. 2012 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00018708_v229_n3_p2098_Carando info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Adv. Math. 2012;229(3):2098-2121 Envelope of holomorphy Holomorphic functions of bounded type Riemann domains Envelopes of holomorphy and extension of functions of bounded type info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v229_n3_p2098_Carando_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v229_n3_p2098_Carando_oai
work_keys_str_mv	AT carandod envelopesofholomorphyandextensionoffunctionsofboundedtype AT muros envelopesofholomorphyandextensionoffunctionsofboundedtype
_version_	1809357037759365120

Envelopes of holomorphy and extension of functions of bounded type

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