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Published version

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1996-06-01

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/164559

On the zero sets of bounded holomorphic functions in the bidisc

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https://doi.org/10.2140/pjm.1996.174.327

Abstract

In this work we prove in a constructive way a theorem of Rudin which says that if $E$ is an analytic subset of the bidisc $D^2$ (with multiplicities) which does not intersect a neighbourhood of the distinguished boundary, then $E$ is the zero set (with multiplicities) of a bounded holomorphic function. This approach allows us to generalize this theorem and also some results obtained by P.S.Chee.

Subject

Funcions holomorfes, Funcions de diverses variables complexes, Espais analítics

Subject (English)

Holomorphic functions, Functions of several complex variables, Analytic spaces

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CHARPENTIER, Philippe and ORTEGA CERDÀ, Joaquim. On the zero sets of bounded holomorphic functions in the bidisc. Pacific Journal of Mathematics. 1996. Vol. 174, num. 2, pags. 327-346. ISSN 0030-8730. [consulted: 11 of June of 2026]. Available at: https://hdl.handle.net/2445/164559

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