Radon inversion on Grassmannians via Gårding-Gindikin fractional integrals
The authors study the Radon transform \(Rf\) of functions on Stiefel and Grassmann manifolds. They establish a connection between \(Rf\) and Gårding-Gindikin fractional integrals associated to the cone of positive definite matrices. By using this connection, they obtain Abel-type representations and explicit inversion formula for \(Rf\) and the corresponding dual Radon transform. The authors work with the space of continuous functions and also with \(Lp\) spaces.
scientific article; zbMATH DE number 2109179