Reduction of dimension as a consequence of norm-resolvent convergence and applications

D. Krejčiřík; N. Raymond; J. Royer; P. Siegl

doi:10.1112/S0025579318000013

Reduction of dimension as a consequence of norm-resolvent convergence and applications

D. Krejčiřík, N. Raymond, J. Royer, P. Siegl

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	406-429
Number of pages	24
Journal	Mathematika
Volume	64
Issue number	2
DOIs	https://doi.org/10.1112/S0025579318000013
Publication status	Published - 2018
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1112/S0025579318000013

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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.",

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AB - 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.

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Reduction of dimension as a consequence of norm-resolvent convergence and applications

Abstract

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