On the \(C^*\)-algebra generated by multidimensional integral operators with homogeneous kernels and multiplicative translations
type: Item
instance of: scholarly article
title: On the \(C^*\)-algebra generated by multidimensional integral operators with homogeneous kernels and multiplicative translations
zbMATH Open document ID: 1163.47059
DOI: 10.1134/S106456240802035X
author: O. G. Avsyankin
published in: Doklady Mathematics
publication date: 2008-10-27T00:00:00Z
review text: The paper investigates the \(C^{\ast}\)-algebra generated by integral operators on \(L_{2}({\mathbb R}^{n})\) with kernel homogeneous of degree \((-n)\) and invariant under the rotation group in \({\mathbb R}^{n}\), and by multiplicative translation operators (operators on the form \(f(x)\rightarrow \delta^{-n/2}f(x/\delta)\), \(\delta>0\)). The author gives a description of the structure of this algebra and constructs a symbolic calculus, in terms of which a criterion of invertibility and Fredholmness is formulated.
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 47L80
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 5357852
zbMATH Keywords: \(C^{\ast}\)-algebra
zbMATH Keywords: integral operator
zbMATH Keywords: homogeneous kernel
zbMATH Keywords: multiplicative translation
zbMATH Keywords: symbol
zbMATH Keywords: symbolic calculus
zbMATH Keywords: Fredholmness
MaRDI profile type: Publication
cites work: Q2723193
cites work: On the algebra of pair integral operators with homogeneous kernels
cites work: Convolution operators and factorization of almost periodic matrix functions
description: scientific article; zbMATH DE number 5357852