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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The envelope of holomorphy of Riemann domains over a countable product of complex planes
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by Mário C. Matos PDF
Trans. Amer. Math. Soc. 167 (1972), 379-387 Request permission

Abstract:

This paper deals with the problem of constructing envelopes of holomorphy for Riemann domains over a locally convex space. When this locally convex space is a countable product of complex planes the existence of the envelope of holomorphy is proved and the domains of holomorphy are characterized.
References
  • Leopoldo Nachbin, Topology on spaces of holomorphic mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 47, Springer-Verlag New York, Inc., New York, 1969. MR 0254579, DOI 10.1007/978-3-642-88511-2
  • H. Alexander, Analytic functions on Banach spaces, Thesis, University of California, Berkeley, Calif., 1968.
  • C. E. Rickart, Analytic functions of an infinite number of complex variables, Duke Math. J. 36 (1969), 581–597. MR 254611, DOI 10.1215/S0012-7094-69-03670-9
  • Jorge Alberto Barroso, Topologies in spaces of holomorphic mappings between locally convex spaces, An. Acad. Brasil. Ci. 43 (1971), 527–546 (Portuguese). MR 308760
  • André Hirschowitz, Remarques sur les ouverts d’holomorphie d’un produit dénombrable de droites, Ann. Inst. Fourier (Grenoble) 19 (1969), no. fasc. 1, 219–229, xi (French, with English summary). MR 252674, DOI 10.5802/aif.314
  • M. C. Matos, Sur l’enveloppe d’holomorphie des domaines de Riemann sur un produit dénombrable de droites, C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A727-A728. MR 42 #3554.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 167 (1972), 379-387
  • MSC: Primary 32D10
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0301235-6
  • MathSciNet review: 0301235