Relatively closed operators associated with a pair of Grassmannians.
type: Item
instance of: scholarly article
title: Relatively closed operators associated with a pair of Grassmannians.
zbMATH Open document ID: 1033.53063
DOI: 10.1023/A:1013974223378
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: Given an incidence relation \(A \subset X \times Y\), it is said that a linear differential operator \(\kappa\) acting on functions on \(Y\) and taking values in differential forms on \(Y\) is relatively closed if it satisfies the relation \(d \kappa(Jf) |_{Y^x} =0\). Here \(f\) is an arbitrary function on \(Y\), \(Jf\) is the integral of \(f\) over \(X^y = (X,y) \cap A\), and \(Y^x = (x,Y) \cap A\). Such operators naturally arise in integral geometry defining local inversion formulas. In the present paper the author considers the case when \(X\) and \(Y\) are Grassmannians and \(A\) is the flag manifold, constructs families of such operators and describes all local inversion formulas for these transformations.
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 1928148
zbMATH Keywords: integral geometry
zbMATH Keywords: local inversion formulas
zbMATH Keywords: relatively closed operator
zbMATH Keywords: Grassmannian
author: M. I. Graev
reviewed by: I. A. Taimanov
MaRDI profile type: Publication
full work available at URL: a:1013974223378
OpenAlex ID: W151044772
description: scientific article; zbMATH DE number 1928148