A Variation of uncertainty principles for the continuous wavelet transform connected with the Riemann–Liouville operator

被引：0
作者：
Khaled Hleili
机构：
[1] Northern Borders University,Department of Mathematics, Faculty of Science
[2] Preparatory Institute for Engineering Studies of Kairouan,Department of Mathematics
来源：
Afrika Matematika | 2023年 / 34卷
关键词：
Wavelet transform; Heisenberg’s type inequality; Donoho–Stark’s uncertainty principles; Local uncertainty principles; Pitt’s inequality; Logarithmic uncertainty principle; 44A05; 42B10;
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摘要：
The aim of this paper is to prove a generalization of uncertainty principles for the continuous wavelet transform connected with the Riemann–Liouville operator in Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-norm. More precisely, we establish the Heisenberg–Pauli–Weyl uncertainty principle, Donoho–Stark’s uncertainty principles and local Cowling-Price’s type inequalities. Finally, Pitt’s inequality and Beckner’s uncertainty principle are proved for this transform.
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  • [1] Baccar C(2006)Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators Int. J. Math. Math. Sci. 2006 1-26
  • [2] Hamadi NB(2008)Best approximation for Weierstrass transform connected with Riemann-Liouville operator Commun. Math. Anal. 5 65-83
  • [3] Rachdi LT(2009)Spaces of Bull. Math. Anal. Appl. 1 16-41
  • [4] Baccar C(1995) type and convolution product associated with the Riemann-Liouville operator Proc. Am. Math. Soc. 123 1897-1905
  • [5] Hamadi NB(2003)Pitt’s inequality and the uncertainty principle Rev. Mat. Iberoamericana 19 23-55
  • [6] Rachdi LT(1984)Hermite functions and uncertainty principles for the Fourier and the widowed Fourier transforms SIAM J. Math. Anal. 15 151-165
  • [7] Baccar C(1989)Bandwidth versus time concentration: the Heisenberg-Pauli-Weyl inequality SIAM J. Appl. Math. 49 906-931
  • [8] Rachdi LT(1978)Uncertainty principles and signal recovery Math. Phys. 19 461-466
  • [9] Beckner W(2013)Inequalities and uncertainty inequalities Integral Transf. Spec. Funct. 24 491-501
  • [10] Bonami A(2014)Uncertainty principles involving Appl. Anal. 93 1057-1072
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