On some $q$-Bessel type continuous wavelet transform

Author:

Mabrouk Anouar BenORCID,Rezgui Imen

Abstract

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.

Publisher

Sociedade Paranaense de Matemática

Reference39 articles.

1. A. Abouelaz, R. Daher and L. El Mehdi, Harmonic Analysis associated with the generalized q-Bessel operator, International Journal of Analysis and Applicayions ISSN 2291-8639, 10 (2016), pp. 17-23.

2. B. Aktan, A. Ben Mabrouk, M. Ozturk, N. Rhaiem, Wavelet-Based systematic risk estimation an application on istanbul stock exchange. International Research Journal of Finance and Economics 23(3) (2009), pp. 33-45.

3. S. Albeverio, P. E. T. Jorgensen, and A. M. Paolucci, Multiresolution wavelet analysis of integer scale Bessel functions J. Math. Phys. 48, 073516 (2007); https://doi.org/10.1063/1.2750291.

4. M. H. Annaby and Z. S. Mansour, q-Fractional Calculus and Equations. Lecture Notes in Mathematics 2056, Editors: J.-M. Morel and B. Teissier, Springer 2012.

5. A. Aral, V. Gupta and R. P. Agarwal, Applications of q-calculs in operator theory, Springer, New York, 2013.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3