On the zero sets of bounded holomorphic functions in the bidisc
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 functi...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1994 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/827 |
| Acceso en línea: | https://hdl.handle.net/2117/827 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 |
| Sumario: | 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. |
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