INTERPOLATION OF CHEBYSHEV POLYNOMIALS AND INTERACTING FOCK SPACES-Reference-Cited by-同舟云学术

INTERPOLATION OF CHEBYSHEV POLYNOMIALS AND INTERACTING FOCK SPACES

Published:2006-09 Issue:03 Volume:09 Page:361-371
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

KUBO IZUMI¹,KUO HUI-HSIUNG²,NAMLI SUAT²

Affiliation:

1. Department of Environmental Design, Faculty of Environmental Studies, Hiroshima Institute of Technology, Hiroshima 731-5193, Japan

2. Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

Abstract

We discover a family of probability measures μa, 0 < a ≤ 1, [Formula: see text] which contains the arcsine distribution (a = 1) and semi-circle distribution (a = 1/2). We show that the multiplicative renormalization method can be used to produce orthogonal polynomials, called Chebyshev polynomials with one parameter a, which reduce to Chebyshev polynomials of the first and second kinds when a = 1 and 1/2 respectively. Moreover, we derive the associated Jacobi–Szegö parameters. This one-parameter family of probability measures coincides with the vacuum distribution of the field operator of the interacting Fock spaces related to the Anderson model.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025706002421

Reference17 articles.

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