On a general q-Fourier transformation with nonsymmetric kernels

Richard A. Askey, Mizan Rahman, Sergeǐ K. Suslov

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

Wiener used the Poisson kernel for the Hermite polynomials to deal with the classical Fourier transform. Askey, Atakishiyev and Suslov used this approach to obtain a q-Fourier transform by using the continuous q-Hermite polynomials. Rahman and Suslov extended this result by taking the Askey-Wilson polynomials, considered to be the most general continuous classical orthogonal polynomials. The theory of q-Fourier transformation is further extended here by considering a nonsymmetric version of the Poisson kernel with Askey-Wilson polynomials. This approach enables us to obtain some new results, for example, the complex and real orthogonalities of these kernels.

Original languageEnglish (US)
Pages (from-to)25-55
Number of pages31
JournalJournal of Computational and Applied Mathematics
Volume68
Issue number1-2
DOIs
StatePublished - Apr 22 1996
Externally publishedYes

Keywords

  • Al-Salam-Chihara polynomials
  • Askey-Wilson polynomials
  • Basic hypergeometric series
  • Fourier transform
  • Hermite polynomials
  • Integral transforms
  • Poisson kernels
  • q-Fourier transform
  • q-orthogonal polynomials

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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