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Harmonic analysis associated to the canonical Fourier Bessel transform
Integral Transforms and Special Functions ( IF 0.7 ) Pub Date : 2020-09-27 , DOI: 10.1080/10652469.2020.1823977
Lazhar Dhaouadi 1 , Jihed Sahbani 2 , Ahmed Fitouhi 2
Affiliation  

ABSTRACT

The aim of this paper is to develop a new harmonic analysis related to a Bessel type operator Δνm on the real line: We define the canonical Fourier Bessel transform Fνm and study some of its important properties. We prove a Riemann–Lebesgue lemma, inversion formula and operational formulas for this transformation. We derive Plancherel theorem and Babenko inequality for Fνm. In the present paper, several uncertainty inequalities and theorems for the canonical Fourier Bessel transform are given, including the Heisenberg inequality, Hardy theorem, Nash-type inequality, Carlson-type inequality, global uncertainty principle, local uncertainty principle, logarithmic uncertainty principle in terms of entropy and Miyachi uncertainty principle.



中文翻译:

与规范傅里叶贝塞尔变换相关的谐波分析

摘要

本文的目的是开发一种与贝塞尔类型算子有关的新谐波分析 Δν 实线:我们定义了经典的傅立叶贝塞尔变换 Fν并研究其一些重要特性。我们证明了这种变换的黎曼-莱贝格引理,反演公式和运算公式。我们推导了Plancherel定理和Babenko不等式Fν 本文给出了经典傅里叶贝塞尔变换的几个不确定性不等式和定理,包括海森堡不等式,哈代定理,纳什型不等式,卡尔森型不等式,全局不确定性原理,局部不确定性原理,对数不确定性原理的熵和宫内不确定性原理。

更新日期:2020-09-27
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