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