Uncertainty principles for the generalized Fourier transform associated to a Dunkl-type operator

被引：9

作者：

Mejjaoli, Hatem ^{[1
]}

机构：

[1] Taibah Univ, Dept Math, Coll Sci, POB 30002, Al Madinah, Al Munawarah, Saudi Arabia

来源：

APPLICABLE ANALYSIS | 2016年 / 95卷 / 09期

关键词：

generalized Fourier transform; Hardy's type theorem; Cowling-Price's theorem; Beurling's theorem; Donoho-Stark's uncertainty principle; variants of Heisenberg's uncertainty principle; DIFFERENTIAL-DIFFERENCE OPERATOR; SPHEROIDAL WAVE-FUNCTIONS; TRANSMUTATION OPERATORS; REAL LINE; THEOREM; SPACES;

D O I：

10.1080/00036811.2015.1080248

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove various mathematical aspects of the qualitative and quantitative uncertainty principle, including Hardy's, Cowling-Price and its variants, Beurling and its variants, Gelfand-Shilov, Donoho-Stark's uncertainty principle, and variants of Heisenberg's inequalities for the generalized Fourier transform associated to a Dunkl-type operator on the real line.

引用

页码：1930 / 1956

页数：27

共 47 条

[1] Qualitative uncertainty principles for the generalized Fourier transform associated to a Dunkl type operator on the real line
Mejjaoli, Hatem
Trimeche, Khalifa
ANALYSIS AND MATHEMATICAL PHYSICS, 2016, 6 (02) : 141 - 162
[2] Paley–Wiener Theorem for a Generalized Fourier Transform Associated to a Dunkl-Type Operator
Minggang Fei
Lan Yang
Mediterranean Journal of Mathematics, 2021, 18
[3] Paley-Wiener Theorem for a Generalized Fourier Transform Associated to a Dunkl-Type Operator
Fei, Minggang
Yang, Lan
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (05)
[4] Qualitative uncertainty principles for the generalized Fourier transform associated to a Dunkl type operator on the real line
Hatem Mejjaoli
Khalifa Trimèche
Analysis and Mathematical Physics, 2016, 6 : 141 - 162
[5] Generalized Wigner transform associated with the Jacobi-Dunkl operator and uncertainty principles
Mejjaoli, Hatem
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2024,
[6] Uncertainty Principles for the Generalized Fourier Transform Associated with Spherical Mean Operator
Hatem Mejjaoli
Youssef Othmani
Analysis in Theory and Applications, 2013, 29 (04) : 309 - 332
[7] QUALITATIVE AND QUANTITATIVE UNCERTAINTY PRINCIPLES FOR THE GENERALIZED FOURIER TRANSFORM ASSOCIATED WITH THE RIEMANN-LIOUVILLE OPERATOR
Mejjaoli, Hatem
Othmani, Youssef
MATEMATICHE, 2016, 71 (02): : 173 - 195
[8] Cowling-Price's and Hardy's uncertainty Principles for the generalized Fourier transform associated to a Cherednik type operator on the real line
Mejjaoli, Hatem
ARCHIV DER MATHEMATIK, 2015, 104 (04) : 377 - 389
[9] Necessary and Sufficient Conditions for the Boundedness of Dunkl-Type Fractional Maximal Operator in the Dunkl-Type Morrey Spaces
Guliyev, Emin
Eroglu, Ahmet
Mammadov, Yagub
ABSTRACT AND APPLIED ANALYSIS, 2010,
[10] Cowling–Price’s and Hardy’s uncertainty Principles for the generalized Fourier transform associated to a Cherednik type operator on the real line
Hatem Mejjaoli
Archiv der Mathematik, 2015, 104 : 377 - 389

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