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On a general q-Fourier transformation with nonsymmetric kernels

Richard A. Askey·Mizan Rahman·Serge\uı K. Suslov
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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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Richard A. Askey, Mizan Rahman, Serge\uı K. Suslov. 1994-11-29. On a general q-Fourier transformation with nonsymmetric kernels. https://arxiv.org/abs/math/9411229

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