Traces of \(G\)-operators concentrated on submanifolds
type: Item
instance of: scholarly article
title: Traces of \(G\)-operators concentrated on submanifolds
zbMATH Open document ID: 1404.35496
DOI: 10.1134/S0012266118040043
author: T. I. Dang
published in: Differential Equations
publication date: 2018-07-20T00:00:00Z
review text: The paper concerns the problem of the definition of the trace of an operator, namely given a manifold \(M\), a submanifold \(X\) and an operator \(P\) on \(M\), one aims to find an operation assigning to \(P\) an operator \(P|_X\), see for example \textit{S. P. Novikov} and \textit{B. Yu. Sternin} [Sov. Math., Dokl. 7, 1373--1376 (1966; Zbl 0174.41302); translation from Dokl. Akad. Nauk SSSR 170, 1265--1268 (1966)]. Here, the author considers the case of a discrete group \(G\) on the manifold \(M\) and operators on \(M\) of the form \[ P= \sum_{g\in G}P_g T_g, \] where \(P_g\) is a sequence of pseudodifferential operators on \(M\) of a fixed order \(m\) and \(T_g\) is the shift operator \(T_gu(x)= u(g^{-1}x)\) induced by an element \(g\in G\). Under a condition on the order \(m\), the author proves that the trace on a submanifold \(X\) is well defined and give for \(P|_X\) a precise expression.
reviewed by: Luigi Rodino
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 6909061
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: discrete groups
zbMATH Keywords: traces on submanifolds
MaRDI profile type: Publication
cites work: Q5562915
cites work: Q5562916
cites work: Q5545733
cites work: Q4693056
cites work: Q3871430
cites work: Q4310044
cites work: Orthogonal decompositions of direct sums and tensor products of algebras
cites work: Elliptic theory and noncommutative geometry. Nonlocal elliptic operators
cites work: Sobolev problems associated with Lie group actions
cites work: Q4265269
cites work: Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds
cites work: Uniformization of nonlocal elliptic operators and \(KK\)-theory
cites work: Index of elliptic operators for diffeomorphisms of manifolds
cites work: Pseudodifferential operators on Hilbert bundles
cites work: On the index of elliptic operators on manifolds with edges
cites work: Q3897569
full work available at URL: s0012266118040043
OpenAlex ID: W2804901199
Recommended article: The trace and the mass of subcritical GJMS operators
Recommended article: Traces of pseudo-differential operators on \(\mathbb{S }^{n-1}\)
Recommended article: Traces of compact operators
Recommended article: On traces of operators associated with actions of compact Lie groups
Recommended article: Traces of operators with a relatively compact perturbation
Recommended article: Sub-elliptic Besov spaces and the characterization of traces on lower dimensional manifolds
Recommended article: Traces of heat operators on Riemannian foliations
Recommended article: Traces of Function Spaces of Fp,q8 — Bp,q8 Type on Submanifolds
Recommended article: Traces on pseudodifferential operators and sums of commutators
description: scientific article; zbMATH DE number 6909061