Orthogonal polynomials and quadratic extremal problems
Author:
J. M. McDougall
Journal:
Trans. Amer. Math. Soc. 354 (2002), 23412357
MSC (2000):
Primary 30A10, 31C25; Secondary 30D55, 33C45, 49J50
Published electronically:
February 1, 2002
MathSciNet review:
1885655
Fulltext PDF Free Access
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Additional Information
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
Email:
JMcDougall@ColoradoCollege.edu
DOI:
http://dx.doi.org/10.1090/S0002994702029604
PII:
S 00029947(02)029604
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
