Proceedings of the American Mathematical Society

Author(s): Saburou Saitoh
Journal: Proc. Amer. Math. Soc. 125 (1997), 3633-3639.
MSC (1991): Primary 30C40
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30C40

Saburou Saitoh
Affiliation: Department of Mathematics, Faculty of Engineering, Gunma University, Kiryu 376, Japan
Email: ssaitoh@eg.gunma-u.ac.jp

DOI: 10.1090/S0002-9939-97-04138-5
PII: S 0002-9939(97)04138-5
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
Copyright of article: Copyright 1997, American Mathematical Society

Saburou Saitoh,Integral transforms,reproducing kernels, and their applications,Applications to representations of inverse functions, Pitman Research Notes in Mathematics Series, vol. 368, First, Addison Wesly Longman Ltd, Harlow, Essex, UK, 1997,pp. 237-242, ?, posted on ?. (English) MR ?

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