Radon inversion on Grassmannians via Gårding-Gindikin fractional integrals
type: Item
instance of: scholarly article
title: Radon inversion on Grassmannians via Gårding-Gindikin fractional integrals
zbMATH Open document ID: 1071.44003
author: Eric L. Grinberg
author: Boris Rubin
published in: Annals of Mathematics. Second Series
publication date: 2004-10-21T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 58C35
zbMATH DE Number: 2109179
zbMATH Keywords: Radon transform
zbMATH Keywords: Stiefel manifold
zbMATH Keywords: Grossmann manifold
zbMATH Keywords: Gårding-Gindikin fractional integrals
zbMATH Keywords: cone of positive definite matrices
zbMATH Keywords: explicit inversion formula
zbMATH Keywords: dual Random transform
reviewed by: Ismail Taqi Ali
MaRDI profile type: Publication
full work available at URL: annals.2004.159.783
OpenAlex ID: W2103631031
DOI: 10.4007/ANNALS.2004.159.783
description: scientific article; zbMATH DE number 2109179