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$ L^p$-nuclear pseudo-differential operators on $ \mathbb{Z}$ and $ \mathbb{S}^1$


Authors: Julio Delgado and M. W. Wong
Journal: Proc. Amer. Math. Soc. 141 (2013), 3935-3942
MSC (2010): Primary 47G30; Secondary 47G10
DOI: https://doi.org/10.1090/S0002-9939-2013-11771-5
Published electronically: July 25, 2013
MathSciNet review: 3091784
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Abstract: Conditions for pseudo-differential operators from $ L^{p_1}(\mathbb{Z})$ into $ L^{p_2}(\mathbb{Z})$ and from $ L^{p_1}({\mathbb{S}}^1)$ into $ L^{p_2}({\mathbb{S}}^1)$ to be nuclear are presented for $ 1\leq p_1$, $ p_2<\infty .$ In the cases when $ p_1=p_2,$ the trace formulas are given.


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Additional Information

Julio Delgado
Affiliation: Departamento de Matemáticas, Universidad del Valle, Calle 13 100-00 Cali, Colombia
Address at time of publication: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Email: julio.delgado@correounivalle.edu.co, j.delgado@imperial.ac.uk

M. W. Wong
Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada
Email: mwwong@mathstat.yorku.ca

DOI: https://doi.org/10.1090/S0002-9939-2013-11771-5
Keywords: Pseudo-differential operators, nuclear operators, 2/3-nuclear operators, traces, Lidskii's formula, eigenvalues
Received by editor(s): October 22, 2011
Received by editor(s) in revised form: January 26, 2012
Published electronically: July 25, 2013
Communicated by: Michael Hitrik
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.