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Transactions of the American Mathematical Society

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Orthogonal polynomials and quadratic extremal problems

Author: J. M. McDougall
Journal: Trans. Amer. Math. Soc. 354 (2002), 2341-2357
MSC (2000): Primary 30A10, 31C25; Secondary 30D55, 33C45, 49J50
Published electronically: February 1, 2002
MathSciNet review: 1885655
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Abstract: The purpose of this paper is to analyse a class of quadratic extremal problems defined on various Hilbert spaces of analytic functions, thereby generalizing an extremal problem on the Dirichlet space which was solved by S.D. Fisher. Each extremal problem considered here is shown to be connected with a system of orthogonal polynomials. The orthogonal polynomials then determine properties of the extremal function, and provide information about the existence of extremals.

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Additional Information

J. M. McDougall
Affiliation: Department of Mathematics and Computer Science, Colorado College, Colorado Springs, Colorado 80903

Received by editor(s): July 7, 1998
Received by editor(s) in revised form: May 8, 2001
Published electronically: February 1, 2002
Article copyright: © Copyright 2002 American Mathematical Society