Espaces symétriques ordonnés et algèbres de Volterra. (Ordered symmetric spaces and Volterra algebras)
type: Item
instance of: scholarly article
title: Espaces symétriques ordonnés et algèbres de Volterra. (Ordered symmetric spaces and Volterra algebras)
zbMATH Open document ID: 0732.43005
published in: Journal of the Mathematical Society of Japan
publication date: 1991-01-01T00:00:00Z
review text: Let \(X=G/H\) be a symmetric space and S a subsemigroup of G which contains H as the largest subgroup. Then S/H forms the positive cone of a left invariant partial ordering on X. A causal kernel on X is a function F: \(X\times X\to {\mathbb{C}}\) which is supported on the graph of the ordering. If the order intervals \(\{\) z: \(x\leq z\leq y\}\) are compact one can form a convolution product of causal kernels and in this way obtain the Volterra algebra, which plays an important role in the harmonic analysis of the space X. The paper under review gives an introduction to the theory and describes a class of symmetric spaces of type \(G_{{\mathbb{C}}}/G_{{\mathbb{R}}}\) to which it applies. Finally the compactness of order intervals is shown for this class.
reviewed by: Joachim Hilgert
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 4210800
zbMATH Keywords: positive cone
zbMATH Keywords: left invariant partial ordering
zbMATH Keywords: convolution product
zbMATH Keywords: causal kernels
zbMATH Keywords: Volterra algebra
zbMATH Keywords: symmetric spaces
zbMATH Keywords: compactness of order intervals
author: Jacques Faraut
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04310133
OpenAlex ID: W2124192818
DOI: 10.2969/JMSJ/04310133
description: scientific article; zbMATH DE number 4210800