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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Analyticity and continuation of certain functions of two complex variables


Author: Carl H. Fitzgerald
Journal: Proc. Amer. Math. Soc. 25 (1970), 536-540
MSC: Primary 32.35
DOI: https://doi.org/10.1090/S0002-9939-1970-0261034-4
MathSciNet review: 0261034
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper shows that the satisfaction of a certain quadratic relation is a sufficient condition that a continuous, symmetric function of two complex variables on a domain be analytic and be continuable to a particular larger domain. This quadratic relation is of the same type as that involved in the Grunsky inequalities.


References [Enhancements On Off] (What's this?)

  • Ju. E. Alenicyn, Univalent functions without common values in a multiply connected domain, Trudy Mat. Inst. Steklov. 94 (1968), 4–18 (Russian). MR 0225989
  • Stefan Bergman, The Kernel Function and Conformal Mapping, Mathematical Surveys, No. 5, American Mathematical Society, New York, N. Y., 1950. MR 0038439
  • S. Bergman and M. Schiffer, Kernel functions and conformal mapping, Compositio Math. 8 (1951), 205–249. MR 39812

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Additional Information

Keywords: Grunsky inequalities, Bergman kernel function, analytic continuation, two complex variables, doubly orthogonal functions
Article copyright: © Copyright 1970 American Mathematical Society