局部域上的Radon反演公式

Unitarization and Inversion Formulae for the Radon Transform between Dual Pairs

We consider the Radon transform associated to dual pairs $(X,Ξ)$ in the sense of Helgason, with $X=G/K$ and $Ξ=G/H$, where $G=\mathbb{R}^d\rtimes K$, $K$ is a closed subgroup of ${\rm GL}(d,\mathbb{R})$ and $H$ is a closed subgroup of $G$. Under some technical assumptions, we prove that if the quasi regular representations of $G$ acting on $L^2(X)$ and $L^2(Ξ)$ are irreducible, then the Radon transform admits a unitarization intertwining the two representations. If, in addition, the representations are square integrable, we provide an inversion formula for the Radon transform based on the voic…

对称空间上的Abel变换、Fourier变换和Radon变换

The Abel, Fourier and Radon transforms on symmetric spaces

本文证明了对称空间上两个Radon变换的一个新的反演定理和一个旧的支撑定理的改进。包括一些新的身份的阿贝尔变换和一些结果有关的傅里叶变换的联合工作与Rawat，Sengupta和Sitaram。

格拉斯曼算子的Capelli恒等式和Radon变换

The Capelli identity and Radon transform for Grassmannians

研究了实除代数上矩形矩阵空间上的一类Capelli型不变微分算子族$C_{s,l}$. $C_{s,l}$在相应的紧致对称空间Grassmannian上退化为不变微分算子，并确定了$C_{s,l}$在Harish-Chandra同态下的像.我们也得到了类似的结果相应的运营商的非紧的Grassmannian，和线丛。作为应用，我们得到了一个Radon反演公式，它推广了B.真正的格拉斯曼人的鲁宾。

The Radon Transform on Function Spaces Related to Homogenous Spaces

We are going to study some conditions on which the Radon transform and its dual are invertible. Two function spaces are introduced that the Radon transform on which is bijective linear operator. In this regards, a reconstruction formula is constructed. Finally the results are supported by an example.

Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces

We consider the horospherical transform and its inversion in 3 examples of hyperboloids. We want to illustrate via these examples the fact that the horospherical inversion formulas can be directly extracted from the classical Radon inversion formula. In a more broad context, this possibility reflects the fact that the harmonic analysis on symmetric spaces (Riemannian as well as pseudo-Riemannian ones) is equivalent (homologous), up to the Abelian Fourier transform, to the similar problem in the flat model. On the technical level it is important that we work not with the usual horospherical tra…

对称空间极限的Radon变换及其对偶

The Radon transform and its dual for limits of symmetric spaces

Radon变换及其对偶是非紧型黎曼对称空间上几何分析的中心对象。在这篇文章中，我们研究对称空间的归纳极限上的这些变换的代数形式。特别地，我们证明了在极限上的某些正则函数空间上存在规范化版本。我们给出了一个公式的归一化变换使用积分核，并将它们与限制的双纤维化变换的领域。