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- W2017777172 abstract "Mehta has shown that eigenvectors [Formula: see text] of the finite Fourier transform with the matrix [Formula: see text], 0 ≤ j, k ≤ N-1, can be defined in terms of the classical Hermite functions [Formula: see text] as [Formula: see text], where [Formula: see text]. We argue that the finite Fourier transform [Formula: see text] does actually govern also some q-extensions of Mehta's eigenvectors [Formula: see text], associated with certain well-known orthogonal q-polynomial families. For the pairs of the continuous q-Hermite and q -1 -Hermite polynomials, the Rogers–Szegő and Stieltjes–Wigert polynomials, and the discrete q-Hermite polynomials of types I and II such links are explicitly derived. In the limit when the base q → 1 these q-extensions coincide with Mehta's eigenvectors [Formula: see text], whereas in the continuous limit (i.e. when the parameter N → ∞) they correspond to the classical Fourier integral transforms between the above-mentioned pairs of q-polynomial families." @default.
- W2017777172 created "2016-06-24" @default.
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- W2017777172 date "2006-09-30" @default.
- W2017777172 modified "2023-09-27" @default.
- W2017777172 title "ON q-EXTENSIONS OF MEHTA'S EIGENVECTORS OF THE FINITE FOURIER TRANSFORM" @default.
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- W2017777172 doi "https://doi.org/10.1142/s0217751x06031673" @default.
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