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

Preprint English OPEN
Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.;

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 t... View more
  • References (28)
    28 references, page 1 of 3

    [1] Wm. R. Allaway, Some properties of the q-Hermite polynomials, Canad. J. Math., Vol. 32, pp. 686-694, 1980.

    [2] G. E. Andrews, R. Askey, and R. Roy, Special Functions, Cambridge University Press, Cambridge, 1999.

    [3] M. Arik, N. M. Atakishiyev, and J. P. Rueda, Discrete q-Hermite polynomials are linked by the integral and finite Fourier transforms, Int. J. Difference Equ., Vol. 1, pp. 195-204, 2006.

    [4] M. Arik and D. D. Coon, Hilbert spaces of analytic functions and generalized coherent states, J. Math. Phys., Vol. 17, pp. 524-527, 1976.

    [5] R. Askey, Continuous q-Hermite polynomials when q > 1, In q-Series and Partitions, Ed. D. Stanton, The IMA Volumes in Mathematics and Its Applications, Vol. 18, pp. 151-158, Springer-Verlag, New York, 1989.

    [6] R. A. Askey and M. E. H. Ismail, A generalization of ultraspherical polynomials, In Studies in Pure Mathematics, Ed. P. Erd˝os, pp. 55-78, Birkh¨auser, Boston, MA, 1983.

    [7] N. M. Atakishiyev, Fourier-Gauss transforms of some q-special functions, CRM Proceedings and Lecture Notes, Vol. 25, pp. 13-21, Amer. Math. Soc., Providence, RI, 2000.

    [8] N. M. Atakishiyev, On q-extensions of Mehta's eigenvectors of the finite Fourier transform, Internat. J. Modern Phys. A, Vol. 21, pp. 4993-5006, 2006.

    [9] N. M. Atakishiyev, D. Galetti, and J. P. Rueda, On relations between certain qpolynomial families, generated by the finite Fourier transform, Int. J. Pure Appl. Math., Vol. 26, pp. 275-284, 2006.

    [10] N. M. Atakishiyev and Sh. M. Nagiev, On the wave functions of a covariant linear oscillator, Theoret. and Math. Phys., Vol. 98, pp.162-166, 1994.

  • Similar Research Results (2)
  • Metrics
    views in OpenAIRE
    views in local repository
    downloads in local repository
Share - Bookmark