On a general q-Fourier transformation with nonsymmetric kernels

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

Research output: Contribution to journalArticle

35 Scopus citations


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
Issue number1-2
StatePublished - Apr 22 1996
Externally publishedYes


  • 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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