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On the zero sets of
bounded holomorphic functions in the bidisc
Philippe Charpentier and Joaquim Ortega-Cerdà |
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Vol. 174 (1996), No. 2, 327–346
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Abstract |
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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 D2 (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. |
Mathematical Subject Classification 2000
Primary: 32A10
Secondary: 32A25, 32C25
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Milestones
Received: 6 December 1993
Revised: 19 May 1995
Published: 1 June 1996
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Authors |
| Philippe Charpentier | |
| Departement de Mathematiques Universite de Bordeaux I 33405 Talence France |
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| Joaquim Ortega-Cerdà | |
| Department of Mathematics Polytechnical University of Cataluna 08028 Barcelona Spain |
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