q-Extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity

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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Bibliographische Detailangaben
Veröffentlicht in:	Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2009-10, Vol.42 (45), p.454004-454004 (9)
Hauptverfasser:	Atakishiyeva, Mesuma K, Atakishiyev, Natig M, Koornwinder, Tom H
Format:	Artikel
Sprache:	eng
Schlagworte:	Construction Eigenvectors Fourier transforms Mathematical analysis Roots Transformations Unity
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Beschreibung
Zusammenfassung:	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.
ISSN:	1751-8121 1751-8113 1751-8121
DOI:	10.1088/1751-8113/42/45/454004