The combinatorial Radon transform modulo the symmetric group

RADON TRANSFORM ON FINITE SYMMETRIC SPACESElinor

The Radon transform belongs to the area of Inverse Problems. The reconstruction of a function from its projection or averages is a central point of study. Besides having direct applications in medical tomography, geophysics, there are also applications in signal processing, statistics and probability. Hence, it is useful to consider discretized versions of the Radon transform.

Radon Transform on Symmetric Matrix Domains

Let X be the matrix unit ball in Mn−k,k(K) consisting of contractive matrices where K = R, C, H. The domain X is a realization of the symmetric space G/K with G = U(n− k, k; K). The matrix ball yo of lower dimension in Mk′−k,k with k ′ ≤ n is a totally geodesic submanifold of X and let Y be the manifold of all G-translations of the submanifold y0. We consider the Radon transform from functions ...

Symmetric powers and the Satake transform

‎This paper gives several examples of the basic functions‎ ‎introduced in recent years by Ng^o‎. ‎These are mainly‎ ‎conjectures based on computer experiment‎.  

The symmetric group - representations, combinatorial algorithms, and symmetric functions

The Radon-gauss Transform

Gaussian measure is constructed for any given hyperplane in an infinite dimensional Hilbert space, and this is used to define a generalization of the Radon transform to the infinite dimensional setting, using Gauss measure instead of Lebesgue measure. An inversion formula is obtained and a support theorem proved.