Elliptic translators on manifolds with point singularities
type: Item
instance of: scholarly article
title: Elliptic translators on manifolds with point singularities
zbMATH Open document ID: 1267.35269
DOI: 10.1134/S001226611212004X
author: Anton Savin
author: Boris Sternin
published in: Differential Equations
publication date: 2013-03-20T00:00:00Z
review text: Consider a smooth closed manifold \(M\) and two closed submanifolds \(Y^p\), \(p= 1,2\), transversally intersecting along a smooth submanifold \(X\), \(\dim X= 0\), \(X\) being the set of singularities of \(Y= Y^1\cup Y^2\). Following the second author, the authors define a pseudodifferential translator \(T_{12}\) acting from \(Y^2\) to \(Y^1\) and develop an elliptic theory for the operators of the form \[ 1+ T: H^s(Y)\to H^s(Y),\quad H^2(Y)= H^{s_1}(Y^1)\oplus H^{s_2}(Y^2). \] The elliptic operators are of Fredholm type (Th. 1) and an index formula for them is found in Th. 2. The index of \((1+T)\) is expressed by the winding number of the invertible on the weight line \(\text{Re\,}z= \alpha\) function \(1+\sigma(T)(z)\), \(\sigma(T)(z)\) being the symbol of corresponding operator family.
Mathematics Subject Classification ID: 35S15
Mathematics Subject Classification ID: 35S35
Mathematics Subject Classification ID: 58J32
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 58B15
zbMATH DE Number: 6147404
zbMATH Keywords: pseudodifferential operator
zbMATH Keywords: boundary value problem
zbMATH Keywords: index of operator
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: boundary manifold with singularities
reviewed by: Peter R. Popivanov
MaRDI profile type: Publication
cites work: Q5545733
cites work: Q5647674
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full work available at URL: s001226611212004x
OpenAlex ID: W1965443201
description: scientific article; zbMATH DE number 6147404