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Abstract:

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.

Registro:

Documento: Artículo
Título:Envelopes of holomorphy and extension of functions of bounded type
Autor:Carando, D.; Muro, S.
Filiación:Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
IMAS, CONICET, Argentina
Palabras clave:Envelope of holomorphy; Holomorphic functions of bounded type; Riemann domains
Año:2012
Volumen:229
Número:3
Página de inicio:2098
Página de fin:2121
DOI: http://dx.doi.org/10.1016/j.aim.2011.10.019
Handle:http://hdl.handle.net/20.500.12110/paper_00018708_v229_n3_p2098_Carando
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.
ISSN:00018708
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00018708_v229_n3_p2098_Carando.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v229_n3_p2098_Carando

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Citas:

---------- APA ----------
Carando, D. & Muro, S. (2012) . Envelopes of holomorphy and extension of functions of bounded type. Advances in Mathematics, 229(3), 2098-2121.
http://dx.doi.org/10.1016/j.aim.2011.10.019
---------- CHICAGO ----------
Carando, D., Muro, S. "Envelopes of holomorphy and extension of functions of bounded type" . Advances in Mathematics 229, no. 3 (2012) : 2098-2121.
http://dx.doi.org/10.1016/j.aim.2011.10.019
---------- MLA ----------
Carando, D., Muro, S. "Envelopes of holomorphy and extension of functions of bounded type" . Advances in Mathematics, vol. 229, no. 3, 2012, pp. 2098-2121.
http://dx.doi.org/10.1016/j.aim.2011.10.019
---------- VANCOUVER ----------
Carando, D., Muro, S. Envelopes of holomorphy and extension of functions of bounded type. Adv. Math. 2012;229(3):2098-2121.
http://dx.doi.org/10.1016/j.aim.2011.10.019