Rudin varieties in products of two annuli
HTML articles powered by AMS MathViewer
- by Sergio E. Zarantonello PDF
- Proc. Amer. Math. Soc. 50 (1975), 174-178 Request permission
Abstract:
Let $Q$ be an annulus and $\partial Q$ its boundary. If $f$ is holomorphic in $Q \times Q$ and its zero set is bounded away from $\partial Q \times \partial Q$, then there exists a bounded holomorphic function $F$ with the same zeros as $f$ such that ${F^{ - 1}}$ is bounded near $\partial Q \times \partial Q$.References
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528
- Walter Rudin, Zero-sets in polydiscs, Bull. Amer. Math. Soc. 73 (1967), 580–583. MR 210934, DOI 10.1090/S0002-9904-1967-11758-0
- E. L. Stout, The second Cousin problem with bounded data, Pacific J. Math. 26 (1968), 379–387. MR 235155
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 174-178
- MSC: Primary 32C25
- DOI: https://doi.org/10.1090/S0002-9939-1975-0379885-9
- MathSciNet review: 0379885