On a general q-Fourier transformation with nonsymmetric kernels

1994/11/29 by Richard Askey, Mizan Rahman, Askey, Richard A. +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.math/9411229

openalex publication_date 1994/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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