The affine group and generalized Gegenbauer polynomials

被引：1

作者：

Feinsilver, P ^{[1
]}

Franz, U

机构：

[1] So Illinois Univ, Dept Math, Carbondale, IL 62901 USA

[2] Univ Greifswald, Inst Math & Informat, D-17487 Greifswald, Germany

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2001年 / 41卷 / 09期

关键词：

affine group; Gegenbauer polynomials; lie algebras;

D O I：

10.1016/S0898-1221(01)00089-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Operators of the form f(xD) - g(L), where L is a shift (lowering) operator, arise naturally in the study of stochastic processes, such as Brownian motion, on the affine group. We find the polynomial eigenfunctions and the action of the affine group as well as the matrix elements uf all exponential function corresponding to L, Then it is determined when the eigenfunctions considered form a family of orthogonal polynomials. (C) 2001 Elsevier Science Ltd. All rights reserved.

引用

页码：1173 / 1182

页数：10

共 9 条

[1]

[Anonymous], 1969, Probability and Mathematical Statistics

[2]

Chihara T. S., 1978, INTRO ORTHOGONAL POL, V13

[3]

DiBucchianico A, 1996, INTEGR TRANSF SPEC F, V4, P49

[4] Duality and multiplicative stochastic processes on quantum groups [J].

Feinsilver, P ;

Franz, U ;

Schott, R .

JOURNAL OF THEORETICAL PROBABILITY, 1997, 10 (03) :795-818

[5]

Feinsilver P., 1992, J THEORET PROBAB, V5, P251

[6]

FRANZ U, 1997, THESIS U H POINCARE, P107

[7]

KNUTH DE, 1991, BILINEAR IDENTITY

[8]

OBERHETTINGER F, 1990, TABLES FOURIER TRANS

[9]

Watson G.N., 1966, TREATISE THEORY BESS

← 1 →