Pointwise convergent expansions in q-Fourier-Bessel series

• Author(s): Abreu, L. D. ; Alvarez-Nodarse, R. ; Cardoso, J. L.
• Date: 2006
• Persistent ID: http://hdl.handle.net/10316/11343
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): q-Fourier series; Third Jackson q-Bessel function
• Document Type: Preprint
• Language: English

Description

We define q-analogues of Fourier-Bessel series, by means of complete q- orthogonal systems constructed with the third Jackson q-Bessel function. Sufficient conditions for pointwise convergence of these series are obtained, in terms of a general convergence principle valid for other Fourier series on grids defined over numerable sets. The results are illustrated with specific examples of developments in q-Fourier-Bessel series.