On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q a root of unity
arXiv:0811.4100 · doi:10.1088/1751-8113/42/45/454004
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.
12 pages, thoroughly rewritten, the q-extended eigenvectors now N-periodic with q an M-th root of 1