Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary

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Title: Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary
Authors: Delgado Valencia, J
Ruzhansky, M
Tokmagambetov, N
Item 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.
Issue Date: 29-Oct-2016
Date of Acceptance: 22-Jul-2016
DOI: https:/d/
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 (
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
Keywords: General Mathematics
0101 Pure Mathematics
0102 Applied Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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