On Some $q$-Bessel Type Continuous Wavelet Transform

Anouar Ben Mabrouk; Imen Rezgui

doi:10.5269/bspm.62547

Anouar Ben Mabrouk University of Tabuk https://orcid.org/0000-0002-2571-1066
Imen Rezgui University of Monastir

Resumo

In this paper we continue as in \cite{Rezguietal} to exploit the modified variants of Bessel function in the framework of $q$-theory to construct wavelet operators. A generalized $q$-Bessel type function has been introduced leading to an associated mother wavelet which in turns has induced a continuous wavelet transform. Finally, Plancherel/Parceval type relations have been proved. Such variants of wavelets permit in some sense to approximate solutions of ODEs and PDEs by transforming them to recurrent sequences.

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Biografia do Autor

Anouar Ben Mabrouk, University of Tabuk

Department of Mathematics

Imen Rezgui, University of Monastir

Department of Mathematics

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