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 language | English (US) |
|---|---|
| Pages (from-to) | 25-55 |
| Number of pages | 31 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 68 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - Apr 22 1996 |
| Externally published | Yes |
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
Fingerprint Dive into the research topics of 'On a general q-Fourier transformation with nonsymmetric kernels'. Together they form a unique fingerprint.
Cite this
Askey, R. A., Rahman, M., & Suslov, S. K. (1996). On a general q-Fourier transformation with nonsymmetric kernels. Journal of Computational and Applied Mathematics, 68(1-2), 25-55. https://doi.org/10.1016/0377-0427(95)00259-6