Intermediate inversion formulas in integral geometry
type: Item
instance of: scholarly article
title: Intermediate inversion formulas in integral geometry
zbMATH Open document ID: 0951.44001
published in: Lobachevskii Journal of Mathematics
publication date: 2000-04-09T00:00:00Z
full work available at URL: https://eudml.org/doc/226798
full work available at URL: graev.html
review text: The aim of the paper is to solve the problem: to reconstruct integrals of a function over \(p\)-dimensional planes in \(\mathbb{R}^n\) starting from its integrals over \(k\)-planes, where \(p< k\). It is proved that for every \(p<k\) there exists an operator \(K_{PK}\) from the space of functions on the manifold \(H_K\) of all \(k\)-dimensional planes into the space of differential \((k-p)\)-forms on \(H_K\) with specific properties. The intermediate inversion formulas are generalized to integral transforms from functions on \(H_P\) to functions on \(H_K\), where \(0\leq p<k\).
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 58A10
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 1413889
zbMATH Keywords: integral geometry
zbMATH Keywords: intermediate problems
zbMATH Keywords: differential forms
zbMATH Keywords: intermediate differential forms
zbMATH Keywords: inversion formulas
zbMATH Keywords: Radon transform
author: M. I. Graev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1413889