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...

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Detalhes bibliográficos
Autores: Charpentier, Philippe, Ortega Cerdà, Joaquim
Formato: artículo
Estado:Versión publicada
Fecha de publicación:1996
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/164559
Acesso em linha:https://hdl.handle.net/2445/164559
Access Level:acceso abierto
Palavra-chave:Funcions holomorfes
Funcions de diverses variables complexes
Espais analítics
Holomorphic functions
Functions of several complex variables
Analytic spaces
Descrição
Resumo: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.