Erdelyi-Kober integrals on the cone of positive definite matrices and Radon transforms on Grassmann manifolds

Details Erdelyi-Kober integrals on the cone of positive definite matrices and Radon transforms on Grassmann manifolds Erdelyi-Kober integrals on the cone of positive definite matrices and Radon transforms on Grassmann manifolds

2008-06-13

arxiv.org/abs/0806.2315v2

Mathematics

Functional Analysis

16 pages

Scientific paper

We introduce bi-parametric fractional integrals of the Erdelyi-Kober type that generalize known Garding-Gindikin constructions associated to the cone of positive definite matrices. It is proved that the Radon transform, which maps a zonal function on the Grassmann manifold $G_{n,m}$ of $m$-dimensional linear subspaces of $R^n$ into a function on the similar manifold $G_{n,k}$, $ 1\leq m

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