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

Published online by Cambridge University Press:  03 April 2018

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.

Type
Research Article
Copyright
Copyright © University College London 2018 

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