A relation between the coefficients in the recurrence formula and the spectral function for orthogonal polynomials-Reference-Cited by-同舟云学术

A relation between the coefficients in the recurrence formula and the spectral function for orthogonal polynomials

Published:1980 Issue:1 Volume:260 Page:65-82
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Geronimo Jeffrey S.

Abstract

A relation is found between the rate of convergence of the coefficients in the recurrence formula for polynomials orthogonal on a segment of the real line and certain properties of the spectral function. The techniques of Banach algebras and scattering theory are used. The close connection between polynomials orthogonal on the unit circle and polynomials orthogonal on the real line is exploited.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1980-260-01/S0002-9947-1980-0570779-9/S0002-9947-1980-0570779-9.pdf

Reference9 articles.

1. A convergence equivalence related to polynomials orthogonal on the unit circle;Baxter, Glen;Trans. Amer. Math. Soc.,1961

2. J. Favard, Sur les polynomes de Tchebycheff, C. R. Acad. Sci. Paris 200 (1935), 2052-2053.

3. G. Freud, Orthogonal polynomials, Pergamon Press, New York, 1971.

4. Scattering theory and polynomials orthogonal on the real line;Geronimo, J. S.;Trans. Amer. Math. Soc.,1980

5. Scattering theory and polynomials orthogonal on the unit circle;Geronimo, J. S.;J. Math. Phys.,1979

Cited by 24 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Structural Algebraic Quantum Field Theory: Particles with Structure;Physics of Particles and Nuclei Letters;2023-12

2. Energy spectrum design and potential function engineering;Theoretical and Mathematical Physics;2023-07

3. Energy spectrum design and potential function engineering;Teoreticheskaya i Matematicheskaya Fizika;2023-07

4. Construction of potential functions associated with a given energy spectrum — An inverse problem II;International Journal of Modern Physics A;2020-09-24

5. Construction of potential functions associated with a given energy spectrum — An inverse problem;International Journal of Modern Physics A;2020-07-13