Generating functions of orthogonal polynomials and Szegö-Jacobi parameters

• Autorzy: Asai N. , Kubo I. , Kuo H.-H.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we present a more direct way to compute the Szegö-Jacobi parameters from a generating function than that in [5] and [6]. Our study is motivated by the notions of one-mode interacting Fock spaces defined in[1] and Segal-Bargmann transform associated with non-Gaussian probability measures introduced in [2]. Moreover, we examine the relationships between the representations of orthogonal polynomials in terms of differential or difference operators and our generating functions. The connections provide practical criteria to determine when functions of a certain form are orthogonal polynomials.

Słowa kluczowe

EN

interacting Fock space; probability measure; orthogonal polynomial; Szegö-Jacobi parameters; pre-generating function; generating function; multiplicative renormalization; differential operators; difference operators

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2003
• Tom: Vol. 23, Fasc. 2
• Strony: 273--291
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Asai N.

• Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

autor

Kubo I.

• Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan
• Department of Environmental Design, Faculty of Environmental Studies, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima, 731-5193, Japan

autor

Kuo H.-H.

• Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.

Bibliografia

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