Uncertainty principles for the Opdam-Cherednik transform on modulation spaces

调制空间上与加窗 Opdam-Cherednik 变换相关的局部化算子

Localization operators associated with the windowed Opdam-Cherednik transform on modulation spaces

本文以加窗 Opdam-Cherednik 变换为基础，在相应调制空间框架下研究依赖符号与双窗函数的时频局部化算子，建立其有界性、紧性及 Schatten-von Neumann 类归属。

分数阶Opdam-Cherednik变换的采样与密度定理

Sampling and Density Theorems for the Fractional Opdam-Cherednik Transform

本文针对分数阶Opdam-Cherednik变换，利用雅可比函数结构构造Riesz基推导采样公式，发展集中算子方法得到密度条件，θ=π/2时可恢复非分数阶对应公式，建立了相关采样与密度理论结果。

Weighted Norm Inequalities for the Opdam--Cherednik Transform

In this paper, we study several weighted norm inequalities for the Opdam--Cherednik transform. We establish different versions of the Heisenberg--Pauli--Weyl inequality for this transform. In particular, we give an extension of this inequality using weights with different exponents and present a variation of the inequality that incorporates $L^p$-norms for the Opdam--Cherednik transform. Also, we prove a version of the Hardy--Littlewood inequality for this transform. Finally, we give other variations of the Heisenberg--Pauli--Weyl inequality such as the Nash-type and Clarkson-type inequalities…

Hausdorff operators associated with the Opdam--Cherednik transform in Lebesgue spaces

In this paper, we introduce the Hausdorff operator associated with the Opdam--Cherednik transform and study the boundedness of this operator in various Lebesgue spaces. In particular, we prove the boundedness of the Hausdorff operator in Lebesgue spaces, in grand Lebesgue spaces, and in quasi-Banach spaces that are associated with the Opdam--Cherednik transform. Also, we give necessary and sufficient conditions for the boundedness of the Hausdorff operator in these spaces.

窗口化Opdam--Cherednik变换的不确定性原理

Uncertainty principles for the windowed Opdam--Cherednik transform

本文针对窗口化Opdam--Cherednik变换建立了多种不确定性原理，包括正交序列、Donoho--Stark、Benedicks型、Heisenberg型及局部不确定性不等式，并利用$k$-熵导出Heisenberg型不等式。

Qualitative uncertainty principles for the windowed Opdam--Cherednik transform on weighted modulation spaces

The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam-Cherednik transform on weighted modulation spaces associated with this transform. In particular, we obtain the Cowling-Price's, Hardy's and Morgan's uncertainty principles for this transform on weighted modulation spaces. The proofs of the results are based on versions of the Phragm{é}n-Lindl{ö}f type result for several complex variables on weighted modulation spaces and the properties of the Gaussian kernel associated with the Jacobi-Cherednik operator.