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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On peak-interpolation manifolds for $\boldsymbol {A}\boldsymbol {(}\boldsymbol {\Omega }\boldsymbol {)}$ for convex domains in $\boldsymbol {\mathbb {C}}^{\boldsymbol {n}}$


Author: Gautam Bharali
Journal: Trans. Amer. Math. Soc. 356 (2004), 4811-4827
MSC (2000): Primary 32A38, 32T25; Secondary 32C25, 32D99
DOI: https://doi.org/10.1090/S0002-9947-04-03705-5
Published electronically: June 22, 2004
MathSciNet review: 2084399
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Abstract: Let $\Omega$ be a bounded, weakly convex domain in ${\mathbb {C}}^n$, $n\geq 2$, having real-analytic boundary. $A(\Omega )$ is the algebra of all functions holomorphic in $\Omega$ and continuous up to the boundary. A submanifold $\boldsymbol {M}\subset \partial \Omega$ is said to be complex-tangential if $T_p(\boldsymbol {M})$ lies in the maximal complex subspace of $T_p(\partial \Omega )$ for each $p\in \boldsymbol {M}$. We show that for real-analytic submanifolds $\boldsymbol {M}\subset \partial \Omega$, if $\boldsymbol {M}$ is complex-tangential, then every compact subset of $\boldsymbol {M}$ is a peak-interpolation set for $A(\Omega )$.


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Additional Information

Gautam Bharali
Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706
Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: bharali@math.wisc.edu, bharali@umich.edu

Keywords: Complex-tangential, finite type domain, interpolation set, pseudoconvex domain
Received by editor(s): July 23, 2002
Published electronically: June 22, 2004
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.