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| Title: | On the zero sets of bounded holomorphic functions in the bidisc |
|---|---|
| Author: | Charpentier, Philippe; Ortega Cerdà, Joaquim |
| Other authors: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
| 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(s): | -Functions of several complex variables -Holomorphic functions -Analytic spaces -Bounded Holomorphic Functions -zero sets -Funcions holomorfes -Espais analítics -Classificació AMS::32 Several complex variables and analytic spaces::32A Holomorphic functions of several complex variables -Classificació AMS::32 Several complex variables and analytic spaces::32C Analytic spaces |
| Rights: | Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
| Document type: | Article |
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