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On the zero sets of bounded holomorphic functions in the bidisc
Charpentier, Philippe; Ortega Cerdà, Joaquim
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
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.
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
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