Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary
File(s)
Published version
Author(s)
Delgado Valencia, J
Ruzhansky, M
Tokmagambetov, N
Type
Journal Article
Abstract
Given a compact manifold M with boundary ∂M, in this paper we
introduce a global symbolic calculus of pseudo-differential operators associated to
(M, ∂M). The symbols of operators with boundary conditions on ∂M are defined in
terms of the biorthogonal expansions in eigenfunctions of a fixed operator L with the
same boundary conditions on ∂M. The boundary ∂M is allowed to have (arbitrary)
singularities. As an application, several criteria for the membership in Schatten
classes on L
2
(M) and r-nuclearity on L
p
(M) are obtained. We also describe a
new addition to the Grothendieck-Lidskii formula in this setting. Examples and
applications are given to operators on M = [0, 1]n with non-periodic boundary
conditions, and of operators with non-local boundary conditions.
introduce a global symbolic calculus of pseudo-differential operators associated to
(M, ∂M). The symbols of operators with boundary conditions on ∂M are defined in
terms of the biorthogonal expansions in eigenfunctions of a fixed operator L with the
same boundary conditions on ∂M. The boundary ∂M is allowed to have (arbitrary)
singularities. As an application, several criteria for the membership in Schatten
classes on L
2
(M) and r-nuclearity on L
p
(M) are obtained. We also describe a
new addition to the Grothendieck-Lidskii formula in this setting. Examples and
applications are given to operators on M = [0, 1]n with non-periodic boundary
conditions, and of operators with non-local boundary conditions.
Date Issued
2016-10-29
Date Acceptance
2016-07-22
Citation
Journal de Mathématiques Pures et Appliquées, 2016, 107 (6), pp.758-783
ISSN
0021-7824
Publisher
Elsevier
Start Page
758
End Page
783
Journal / Book Title
Journal de Mathématiques Pures et Appliquées
Volume
107
Issue
6
Copyright Statement
© 2016 The Authors. Published by Elsevier Masson
SAS. This is an open access article under the
CC-BY license (http://creativecommons.org/licenses/by/4.0/).
SAS. This is an open access article under the
CC-BY license (http://creativecommons.org/licenses/by/4.0/).
Sponsor
Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Grant Number
EP/K039407/1
RPG-2014-002
Subjects
General Mathematics
0101 Pure Mathematics
0102 Applied Mathematics
Publication Status
Published