Some Generalized $q$-Bessel Type Wavelets and Associated Transforms Article Swipe

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Bessel function Wavelet Context (archaeology) Mathematics Extension (predicate logic) Type (biology) Bessel process Pure mathematics Mathematical analysis Legendre wavelet Wavelet transform Discrete wavelet transform Computer science Artificial intelligence Gegenbauer polynomials Orthogonal polynomials Paleontology Biology Programming language Ecology Classical orthogonal polynomials

Imen Rezgui , Anouar Ben Mabrouk ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1705.00236 · OA: W2611153157

In this paper wavelet functions are introduced in the context of $q$-theory. We precisely extend the case of Bessel and $q$-Bessel wavelets to the generalized $q$-Bessel wavelets. Starting from the $(q,v)$-extension ($v=(α,β)$) of the $q$-case, associated generalized $q$-wavelets and generalized $q$-wavelet transforms are then developed for the new context. Reconstruction and Plancherel type formulas are proved.