TY - JOUR
T1 - Some Generalized $q$-Bessel Type Wavelets and Associated Transforms
AU - Imen Rezgui & Anouar Ben Mabrouk
JO - Analysis in Theory and Applications
VL - 1
SP - 57
EP - 76
PY - 2018
DA - 2018/07
SN - 34
DO - http://doi.org/10.4208/ata.2018.v34.n1.5
UR - https://global-sci.org/intro/article_detail/ata/12545.html
KW - Wavelets, Besel function, $q$-Bessel function, modified Bessel functions, generalized $q$-Bessel functions, $q$-Bessel wavelets.
AB - <p style="text-align: justify;">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 developed for the new
context. Reconstruction and Placherel type formulas are proved.</p>