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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 the modulus of boundary values of holomorphic functions
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by R. Michael Range PDF
Proc. Amer. Math. Soc. 65 (1977), 282-286 Request permission

Abstract:

A differential geometric method is introduced to study the modulus of boundary values of holomorphic functions on smoothly bounded pseudoconvex domains D in ${{\mathbf {C}}^n},n \geqslant 2$. It is shown that functions in $A(D)$ are determined up to a constant factor by their modulus on an open subset of the Shilov boundary. For the case of ${H^\infty }(D)$, it is shown that inner functions which satisfy a certain local condition are constant.
References
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 65 (1977), 282-286
  • MSC: Primary 32A10
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0457758-2
  • MathSciNet review: 0457758