R上对偶Dunkl-Sonine变换的Dunkl小波反演

实直线上Dunkl核的Sonine变换

Sonine Transform Associated to the Dunkl Kernel on the Real Line

考虑Dunkl交织算子$V_α$及其对偶${}^tV_α$，定义并研究了$\mathbb{R}$上的Dunkl Sonine算子及其对偶.其次，我们引入了Dunkl-Laplacian算子$Δ_α$的复幂，建立了Dunkl-Sonine算子$S_{α,β}$及其对偶${}^tS_{α,β}$的反演公式.此外，我们还给出了算子${}^tS_{α,β}$的Plancherel公式.

Sonine formulas and intertwining operators in Dunkl theory

Let $V_k$ denote Dunkl's intertwining operator associated with some root system $R$ and multiplicity function $k$. For two multiplicities $k, k^\prime$ on $R$, we study the operator $V_{k^\prime,k} = V_{k^\prime}\circ V_k^{-1}$, which intertwines the Dunkl operators for multiplicity $k$ with those for multiplicity $k^\prime.$ While it is well-known that the operator $V_k$ is positive for nonnegative $k$, it has been a long-standing conjecture that its generalizations $V_{k^\prime,k}$ are also positive if $k^\prime \geq k \geq 0,$ which is known to be true in rank one. In this paper, we disprov…

连续线性正则 Dunkl 小波变换：性质与应用

Continous linear canonical Dunkl wavelet transform: properties and applications

本文建立线性正则 Dunkl 小波变换，引入广义平移与卷积，研究其性质并推导不确定性不等式。

球面Radon-Dunkl变换的反演公式

Inversion Formulas for the Spherical Radon-Dunkl Transform

引入了与权函数在有限反射群下不变相关联的球面Radon-Dunkl变换$R_κ$，并利用$h$ -调和函数得到了它的一些基本性质.借助于球面Riesz-Dunkl势、Dunkl算子和适当的小波变换，给出了$R_κ$的几种反演公式。