$q$-Bessel Fourier Transform and Variation Diminishing kernel
Lazhar Dhaouadi, Saidani Islem, Hedi Elmonser
TL;DR
This paper explores the $q$-Bessel Fourier Transform and introduces a new $q$-special function, the $q$-Macdonald function, to analyze variation diminishing kernels within $q$-calculus.
Contribution
It introduces the $q$-Macdonald function, a novel $q$-special function, and applies it to study variation diminishing kernels in $q$-calculus.
Findings
Defined the $q$-Macdonald function as a new $q$-special function.
Analyzed properties of the variation diminishing kernel in the $q$-calculus context.
Established the role of the $q$-Macdonald function in the $q$-Bessel Fourier Transform.
Abstract
In this paper we study the variation diminishing kernel as a part of the -calculus. We introduce the -Macdonald function a newborne in the family of the -special functions which play a central role in this study.
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Taxonomy
TopicsMathematical functions and polynomials · Nonlinear Waves and Solitons · Mathematical Analysis and Transform Methods