The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (250 KB) | Metadata | Table of Contents | ZAA summary
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