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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 3, 2001, pp. 761–775
DOI: 10.4171/ZAA/1044

Published online: 2001-09-30

Orthogonality and Completeness of $q$-Fourier Type Systems

Mourad E. H. Ismail[1]

(1) University of Central Florida, Orlando, United States

We establish orthogonality and completeness of the system of $q$-exponential functions {$\mathcal E_q(\cdot; i\omega_n)$} using orthogonality and dual orthogonality of a $q$-analogue of Lommel polynomials. We also set up a very general procedure by which one can produce similar orthogonal systems using bilinear generating functions formed by products of two complete orthogonal function systems.

Keywords: Continuous $q$-ultraspherical polynomials, $q$-exponential functions, orthogonality, completeness, discrete orthogonal polynomials, dual orthogonality

Ismail Mourad: Orthogonality and Completeness of $q$-Fourier Type Systems. Z. Anal. Anwend. 20 (2001), 761-775. doi: 10.4171/ZAA/1044