Donoho–Stark and Price uncertainty principles for a class of <i>q</i>-integral transforms with bounded kernels-Reference-Cited by-同舟云学术

Donoho–Stark and Price uncertainty principles for a class of q-integral transforms with bounded kernels

Published:2024-01-02 Issue:0 Volume:0 Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Castro Luis P.¹^ORCID,Guerra Rita C.²^ORCID

Affiliation:

1. Center for Research and Development in Mathematics and Applications (CIDMA) , Department of Mathematics , University of Aveiro , Aveiro , Portugal

2. Center for Research and Development in Mathematics and Applications (CIDMA) , Department of Mathematics , University of Aveiro , Aveiro ; and Coimbra Business School, Polytechnic Institute of Coimbra, Coimbra , Portugal

Abstract

Abstract We consider a very global q-integral transform, essentially characterized by having a bounded kernel and satisfying a set of natural and useful properties for the realization of applications. The main ambition of this work is to seek conditions that guarantee uncertainty principles of the Donoho–Stark type for that class of q-integral transforms. It should be noted that the global character of the q-integral transform in question allows one to immediately deduce corresponding Donoho–Stark uncertainty principles for q-integral operators that are its particular cases. These particular cases are very well-known operators, namely: a q-cosine-Fourier transform, a q-sine-Fourier transform, a q-Fourier transform, a q-Bessel–Fourier transform and a q-Dunkl transform. Moreover, generalizations of the local uncertainty principle of Price for the q-cosine-Fourier transform, q-sine-Fourier transform, q-Fourier transform, q-Bessel–Fourier transform and q-Dunkl transform are also obtained.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2023-0244/pdf

Reference24 articles.

1. A. Achak, A. Abouelaz, R. Daher and N. Safouane, Quantitative uncertainty principles related to Lions transform, Arnold Math. J. 8 (2022), no. 3–4, 481–496.

2. N. Bettaibi, Uncertainty principles in q 2 q^{2} -analogue Fourier analysis, Math. Sci. Res. J. 11 (2007), no. 11, 590–602.

3. N. Bettaibi and R. Bettaieb, q-analogue of the Dunkl transform on the real line, Tamsui Oxf. J. Math. Sci. 25 (2009), no. 2, 177–205.

4. P. Boggiatto, E. Carypis and A. Oliaro, Two aspects of the Donoho–Stark uncertainty principle, J. Math. Anal. Appl. 434 (2016), no. 2, 1489–1503.

5. K. Brahim and B. Anis, On uncertainty principle of orthonormal sequences for the q-Dunkl transform, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 80 (2018), no. 1, 25–32.