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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Detalles Bibliográficos
Autores: Charpentier, Philippe, Ortega Cerdà, Joaquim
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1996
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/164559
Acceso en línea:https://hdl.handle.net/2445/164559
Access Level:acceso abierto
Palabra clave:Funcions holomorfes
Funcions de diverses variables complexes
Espais analítics
Holomorphic functions
Functions of several complex variables
Analytic spaces
Descripción
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.