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

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

2008-11-25

arxiv.org/abs/0811.4100v2

J. Phys. A 42 (2009) 454004

Mathematics

Classical Analysis and ODEs

12 pages, thoroughly rewritten, the q-extended eigenvectors now N-periodic with q an M-th root of 1

Scientific paper

10.1088/1751-8113/42/45/454004

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.

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