Representations of inverse functions
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- by Saburou Saitoh PDF
- Proc. Amer. Math. Soc. 125 (1997), 3633-3639 Request permission
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.References
- P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
- Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X
- Stefan Bergman, The kernel function and conformal mapping, Second, revised edition, Mathematical Surveys, No. V, American Mathematical Society, Providence, R.I., 1970. MR 0507701
- Saburou Saitoh, Hilbert spaces induced by Hilbert space valued functions, Proc. Amer. Math. Soc. 89 (1983), no. 1, 74–78. MR 706514, DOI 10.1090/S0002-9939-1983-0706514-9
- Saburou Saitoh, Theory of reproducing kernels and its applications, Pitman Research Notes in Mathematics Series, vol. 189, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. MR 983117
- Saburou Saitoh, Decreasing principles in transforms of reproducing kernel Hilbert spaces, Math. Montisnigri 1 (1993), 99–109. MR 1252576
Additional Information
- Saburou Saitoh
- Email: ssaitoh@eg.gunma-u.ac.jp
- Received by editor(s): May 15, 1995
- Received by editor(s) in revised form: July 15, 1996
- Communicated by: Theodore W. Gamelin
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 3633-3639
- MSC (1991): Primary 30C40
- DOI: https://doi.org/10.1090/S0002-9939-97-04138-5
- MathSciNet review: 1423330