Abstract
In this article we define and construct the ϑ-envelope of holomorphy of X for every type ϑ where X is a Riemann domain over a complex Banach space E.
We first show that if X is an open connected subset of a Banach space E, then there exists a ϑ-envelope of holomorphy, unique up to isomorphism. Next we extend the result to any connected Riemann domain over a Banach space E.
The method is about the same as that used by P. Noverraz in
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Alexander, H., Analytic Functions on Banach Spaces, Thesis, University of California at Berkeley (1968).
Hirschowitz, A., Prolongement Analytique en Dimension Infinie, C.R. Acad. Sc. Paris, t. 270 (1970) Série A, pp. 1736–1737.
Matos, M.C., Holomorphic Mappings and Domains of Holomorphy, Monografias do Centro Brasileiro de Pesquisas Físicas, no27, Rio de Janeiro (1970).
Nachbin, L., Holomorphic Functions, Domains of Holomorphy and Local Properties, North-Holland, 1970.
Narasimhan, R., Several Complex Variables, Chicago Lectures in Mathematics-The University of Chicago Press (1971).
Noverraz, P., Pseudo-Convexité, Convexité Polynomiale et Domaines d'Holomorphie en Dimension Infinie, Notas de Matemática, Vol. 48 (1973), North-Holland.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Moraes, L.A. (1981). Envelopes for types of holomorphy. In: Machado, S. (eds) Functional Analysis, Holomorphy, and Approximation Theory. Lecture Notes in Mathematics, vol 843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089286
Download citation
DOI: https://doi.org/10.1007/BFb0089286
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10560-2
Online ISBN: 978-3-540-38529-5
eBook Packages: Springer Book Archive