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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Generalized functions and orthogonal polynomials on the unit circle


Author: Ahmed I. Zayed
Journal: Proc. Amer. Math. Soc. 88 (1983), 407-415
MSC: Primary 42C05; Secondary 33A65, 46F10
MathSciNet review: 699404
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Abstract: In a recent paper, R. Morton and A. Krall introduced a new notion of orthogonality of polynomials on the real line in which a sequence of Chebyshev-type polynomials was shown to be orthogonal with respect to a moment generating linear functional. This linear functional is, in fact, a Schwartz distribution. If the polynomials are orthogonal in the classical sense, then the classical weight function can be recovered from the distributional one by means of the Fourier transform.

The purpose of this paper is to study the analogue of their results for polynomials orthogonal on the unit circle.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699404-1
PII: S 0002-9939(1983)0699404-1
Keywords: Generalized functions, orthogonal polynomials
Article copyright: © Copyright 1983 American Mathematical Society