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Matrix transformations of series of orthogonal polynomials

Part of: Geometric function theory

Published online by Cambridge University Press:  26 February 2010

David Borwein ,
Peter Borwein  and
Ammon Jakimovski
David Borwein
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario, Canada.
Peter Borwein
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada, VSA 1S6.
Ammon Jakimovski
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel.
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Abstract

For a sequence of polynomials (Pn) orthonormal on the interval [−1, 1], we consider the sequence of transforms (gn) of the series given by . We establish necessary and sufficient conditions on the matrix (bnk) for the sequence (gn) to converge uniformly on compact subsets of the interior of an appropriate ellipse to a function holomorphic on that interior.

MSC classification

Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Mathematika , Volume 42 , Issue 2 , December 1995 , pp. 427 - 443
Copyright
Copyright © University College London 1995

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