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Volume 34, Issue 1
Some Generalized $q$-Bessel Type Wavelets and Associated Transforms

Imen Rezgui & Anouar Ben Mabrouk

DOI: 10.4208/ata.2018.v34.n1.5

Anal. Theory Appl., 34 (2018), pp. 57-76.

Published online: 2018-07

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  • Abstract

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.

  • Keywords

Wavelets, Besel function, $q$-Bessel function, modified Bessel functions, generalized $q$-Bessel functions, $q$-Bessel wavelets.

  • AMS Subject Headings

42A38, 42C40, 33D05, 26D15

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-34-57, author = {Imen Rezgui and Anouar Ben Mabrouk}, title = {Some Generalized $q$-Bessel Type Wavelets and Associated Transforms}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {1}, pages = {57--76}, abstract = {

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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2018.v34.n1.5}, url = {http://global-sci.org/intro/article_detail/ata/12545.html} }
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 -

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.

Imen Rezgui and Anouar Ben Mabrouk. (2018). Some Generalized $q$-Bessel Type Wavelets and Associated Transforms. Analysis in Theory and Applications. 34 (1). 57-76. doi:10.4208/ata.2018.v34.n1.5
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