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Peaking and interpolation by complex polynomials

Part of: Geometric function theory Miscellaneous topics of analysis in the complex domain

Published online by Cambridge University Press:  05 May 2021

Thomas H. MacGregor  and
Michael P. Sterner
Thomas H. MacGregor
Affiliation:
State University of New York at Albany, Professor Emeritus, 60 S. Washington St., Athens, NY12015, USA
Michael P. Sterner
Affiliation:
Department of Biology, Chemistry, and Mathematics, University of Montevallo, Station 6493, Harman Hall, Montevallo, AL35115, USA ([email protected])
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Abstract

Classical results about peaking from complex interpolation theory are extended to polynomials on a closed disk, and on the complement of its interior. New results are obtained concerning interpolation by univalent polynomials on a Jordan domain whose boundary satisfies certain smoothness conditions.

Keywords

peakingunivalent functionsinterpolationpolynomials

MSC classification

Primary: 30E05: Moment problems, interpolation problems 30C10: Polynomials
Secondary: 30C20: Conformal mappings of special domains
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 2 , May 2021 , pp. 129 - 138
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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