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Orthogonal polynomials and quadratic extremal problems
Author(s):
J.
M.
McDougall
Journal:
Trans. Amer. Math. Soc.
354
(2002),
2341-2357.
MSC (2000):
Primary 30A10, 31C25;
Secondary 30D55, 33C45, 49J50
Posted:
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.
References:
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- 2.
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- 3.
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- 4.
- Bateman Manuscript Project, Higher Transcendental Functions, McGraw-Hill Book Company, N.Y., Vols. 1,2, 1953, Vol. 3, 1955. MR 15:419i; MR 16:586c
- 5.
- S.D. Fisher, A Quadratic Extremal Problem on the Dirichlet Space, Complex Variables Theory Appl., 1995, 26, pp. 367-380. MR 96i:30030
- 6.
- I.C. Gohberg and M.G. Krein, Introduction to the Theory of Linear Non-Self Adjoint Operators, Transl. Math. Monos., vol. 18, Amer. Math. Soc., 1969. MR 39:7447
- 7.
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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:
10.1090/S0002-9947-02-02960-4
PII:
S 0002-9947(02)02960-4
Received by editor(s):
July 7, 1998
Received by editor(s) in revised form:
May 8, 2001
Posted:
February 1, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
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