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REDUCTION OF DIMENSION AS A CONSEQUENCE OF NORM-RESOLVENT CONVERGENCE AND APPLICATIONS

Part of: Partial differential equations on manifolds; differential operators General mathematical topics and methods in quantum theory Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  03 April 2018

D. Krejčiřík ,
N. Raymond ,
J. Royer  and
P. Siegl
D. Krejčiřík
Affiliation:
Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 12000 Prague 2, Czech Republic email david.krejcirik@fjfi.cvut.cz
N. Raymond
Affiliation:
IRMAR, Université de Rennes 1, Campus de Beaulieu, F-35042 Rennes cedex, France email nicolas.raymond@univ-rennes1.fr
J. Royer
Affiliation:
Institut de Mathématiques de Toulouse, Université Toulouse 3, 118 route de Narbonne, F-31062 Toulouse cedex 9, France email julien.royer@math.univ-toulouse.fr
P. Siegl
Affiliation:
Mathematical Institute, University of Bern, Alpeneggstrasse 22, 3012 Bern, Switzerland email petr.siegl@math.unibe.ch On leave from Nuclear Physics Institute ASCR, 25068 Řež, Czech Republic
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Abstract

This paper is devoted to dimensional reductions via the norm-resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The efficiency of our abstract tool is demonstrated by its application on seemingly different partial differential equation problems from various areas of mathematical physics; all are analysed in a unified manner, known results are recovered and new ones established.

MSC classification

Primary: 81Q15: Perturbation theories for operators and differential equations
Secondary: 35P05: General topics in linear spectral theory 35P20: Asymptotic distribution of eigenvalues and eigenfunctions 58J50: Spectral problems; spectral geometry; scattering theory 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis 81Q20: Semiclassical techniques, including WKB and Maslov methods
Type
Research Article
Information
Mathematika , Volume 64 , Issue 2 , 2018 , pp. 406 - 429
Copyright
Copyright © University College London 2018 

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