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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Orthogonal polynomials and quadratic extremal problems
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by J. M. McDougall PDF
Trans. Amer. Math. Soc. 354 (2002), 2341-2357 Request permission


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:
  • Received by editor(s): July 7, 1998
  • Received by editor(s) in revised form: May 8, 2001
  • Published electronically: February 1, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2341-2357
  • MSC (2000): Primary 30A10, 31C25; Secondary 30D55, 33C45, 49J50
  • DOI:
  • MathSciNet review: 1885655