IJPAM: Volume 26, No. 2 (2006)

ON RELATIONS BETWEEN CERTAIN $q$-POLYNOMIAL
FAMILIES, GENERATED BY THE FINITE
FOURIER TRANSFORM

N.M. Atakishiyev$^1$, Diogenes Galetti$^{2}$, Juvenal P. Rueda$^3$
$^{1,3}$Instituto de Matemáticas
UNAM - Universidad Nacional Autonoma de Mexico
Apartado Postal 273-3, C.P. 62210
Cuernavaca, Morelos, MEXICO
$^1$e-mail: natig@matcuer.unam.mx
$^2$Instituto de Física Teórica
Universidade Estadual Paulista - UNESP
Rua Pamplona 145
01405 - São Paulo - SP, BRAZIL
e-mail: galetti@ift.unesp.br


Abstract.Some $q$-extensions of Mehta's eigenvectors of the finite Fourier transform are studied. It is shown that the finite Fourier transform operator interrelates certain well-known $q$-polynomial families.

Received: December 12, 2005

AMS Subject Classification: 33D45, 39A13, 42C30

Key Words and Phrases: finite Fourier transform, eigenvectors, theta-function, $q$-Hermite polynomials, Rogers-Szego polynomials, Stieltjes-Wigert polynomials

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 2