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Proceedings of the American Mathematical Society

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



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
MathSciNet review: 0261034
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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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Keywords: Grunsky inequalities, Bergman kernel function, analytic continuation, two complex variables, doubly orthogonal functions
Article copyright: © Copyright 1970 American Mathematical Society