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Proceedings of the American Mathematical Society

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Operator-valued typically real functions

Author: Ky Fan
Journal: Proc. Amer. Math. Soc. 124 (1996), 765-771
MSC (1991): Primary 30-XX, 47-XX
MathSciNet review: 1285989
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Abstract: Generalizing the classical typically real functions in complex analysis, we introduce the operator-valued typically real functions and show how to construct these functions.

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

  • [1] Peter L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983. MR 708494
  • [2] M. Naimark, Positive definite operator functions on a commutative group, Izv. Akad. Nauk SSSR Math. Ser. 7 (1943), 237--244.
  • [3] Christian Pommerenke, Univalent functions, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen; Studia Mathematica/Mathematische Lehrbücher, Band XXV. MR 0507768
  • [4] W. Rogosinski, Über positive harmonische Entwicklungen und typisch-reelle Potenzreihen, Math. Z. 35 (1932), 93--121.

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Additional Information

Ky Fan
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Address at time of publication: 1402 Santa Teresita Drive, Santa Barbara, California 93105-1948

Received by editor(s): June 14, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society