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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On boundary values of holomorphic functions on balls
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by Josip Globevnik PDF
Proc. Amer. Math. Soc. 85 (1982), 61-64 Request permission

Abstract:

It is a result of Agranovski and Valski for which Nagel and Rudin, and Stout have given alternate proofs, that if $B$ is the open unit ball in ${{\mathbf {C}}^n}$ and if $f \in C(\partial B)$ has the property that for every complex line $\Lambda \subset {{\mathbf {C}}^n}$, $f\left | {(\Lambda \cap \partial B)} \right .$ has a continuous extension to $\Lambda \cap \bar B$ which is holomorphic in $\Lambda \cap B$, then $f$ has a continuous extension to $\bar B$ which is holomorphic in $B$. In the paper we give an easier, more geometric proof of this result and then prove the local version of this result.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 61-64
  • MSC: Primary 32A40
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0647898-9
  • MathSciNet review: 647898