On a q-extension of Mehta's eigenvectors of the finite Fourier transform
  for q a root of unity

Allaway Wm R; Andrews G E; Arik M; Askey R; Askey R A; Atakishiyev N M; Atakishiyev N M; Atakishiyev N M; Berndt B; Biedenharn L C; Dahlquist G; Gasper G; Koekoek R Swarttouw R F; Lidl R; Macfarlane A J; Matveev V B; Mesuma K Atakishiyeva; Natig M Atakishiyev; Serre J-P; Stein E; Terras A; Tom H Koornwinder

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On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q a root of unity

Authors: Allaway Wm R
Andrews G E
Arik M
Askey R
Askey R A
Atakishiyev N M
Atakishiyev N M
Atakishiyev N M
Berndt B
Biedenharn L C
Dahlquist G
Gasper G
Koekoek R Swarttouw R F
Lidl R
Macfarlane A J
Matveev V B
Mesuma K Atakishiyeva
Natig M Atakishiyev
Serre J-P
Stein E
Terras A
Tom H Koornwinder
Publication date: 1 January 2009
Publisher: 'IOP Publishing'
Doi

Abstract

It is shown that the continuous q-Hermite polynomials for q a root of unity have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.Comment: 12 pages, thoroughly rewritten, the q-extended eigenvectors now N-periodic with q an M-th root of