Fourier multipliers, symbols and nuclearity on compact manifolds

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Title: Fourier multipliers, symbols and nuclearity on compact manifolds
Author(s): Delgado Valencia, JC
Ruzhansky, M
Item Type: Journal Article
Abstract: The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. As a consequence, given a compact manifold M endowed with a positive measure, we introduce a notion of the operator's full symbol adapted to the Fourier analysis relative to a fixed elliptic operator E. We give a description of Fourier multipliers, or of operators invariant relative to E. We apply these concepts to study Schatten classes of operators on L2 (M) and to obtain a formula for the trace of trace class operators. We also apply it to provide conditions for operators between Lp-spaces to be r-nuclear in the sense of Grothendieck.
Publication Date: 1-Jun-2018
Date of Acceptance: 7-Dec-2015
URI: http://hdl.handle.net/10044/1/42525
DOI: https://dx.doi.org/10.1007/s11854-018-0052-9
ISSN: 0021-7670
Publisher: Springer Verlag (Germany)
Start Page: 757
End Page: 800
Journal / Book Title: Journal d'Analyse Mathematique
Volume: 135
Issue: 2
Copyright Statement: © The author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Sponsor/Funder: Commission of the European Communities
Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: 301599
EP/K039407/1
RPG-2014-002
Keywords: Science & Technology
Physical Sciences
Mathematics
VON-NEUMANN PROPERTIES
PSEUDODIFFERENTIAL-OPERATORS
RIEMANNIAN-MANIFOLDS
SCHATTEN CLASSES
WEYL CALCULUS
SPACES
GROTHENDIECK
TRACES
NORM
LP
math.FA
math.FA
math.AP
math.SP
Primary 35S05, 58J40, Secondary 22E30, 47B06, 47B10
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Online Publication Date: 2018-08-07
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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