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Proceedings of the American Mathematical Society

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



Representations of inverse functions

Author: Saburou Saitoh
Journal: Proc. Amer. Math. Soc. 125 (1997), 3633-3639
MSC (1991): Primary 30C40
MathSciNet review: 1423330
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Abstract: Let $\phi : \hat E \rightarrow E$ be an arbitrary map from an abstract set $\hat E$ into an abstract set $E$. We shall use the theory of reproducing kernels to provide a general method for representing the inverse map $\phi ^{-1}$ in terms of $\phi $. We give several concrete examples of this method.

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Saburou Saitoh

Keywords: Inverse function, reproducing kernel, the Riemann mapping function, Bergman kernel, Szeg\"{o} kernel, multi-valued function, harmonic mapping, increasing function
Received by editor(s): May 15, 1995
Received by editor(s) in revised form: July 15, 1996
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society