Uniform convergence of Fourier-Bessel series on a q-linear grid
L. D. Abreu, R. \'Alvarez-Nodarse, J. L. Cardoso
TL;DR
This paper investigates the uniform convergence of Fourier-Bessel series on a q-linear grid, providing conditions for convergence and illustrating results with specific q-Fourier-Bessel series examples.
Contribution
It introduces sufficient conditions for uniform convergence of Fourier-Bessel series on q-linear grids using third Jackson q-Bessel functions.
Findings
Established convergence conditions for Fourier-Bessel series
Provided examples demonstrating convergence behavior
Extended understanding of q-orthogonal system expansions
Abstract
We study Fourier-Bessel series on a q-linear grid, defined as expansions in complete q-orthogonal systems constructed with the third Jackson q-Bessel function, and obtain sufficient conditions for uniform convergence. The convergence results are illustrated with specific examples of expansions in q-Fourier-Bessel series.
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Taxonomy
TopicsMathematical functions and polynomials · Approximation Theory and Sequence Spaces · Mathematical Analysis and Transform Methods