A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains

J. Behrndt, M. Langer, I. Lobanov, V. Lotoreichik, I. Yu. Popov

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In this note we investigate the asymptotic behavior of the s-numbers of the resolvent difference of two generalized self-adjoint, maximal dissipative or maximal accumulative Robin Laplacians on a bounded domain Ω with smooth boundary ∂Ω. For this we apply the recently introduced abstract notion of quasi boundary triples and Weyl functions from extension theory of symmetric operators together with Krein type resolvent formulae and well-known eigenvalue asymptotics of the Laplace-Beltrami operator on ∂Ω. It is shown that the resolvent difference of two generalized Robin Laplacians belongs to the Schatten-von Neumann class of any order p for which
LanguageEnglish
Pages750-758
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume371
Issue number2
DOIs
Publication statusPublished - 2010

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Resolvent
Mathematical operators
Bounded Domain
Eigenvalue Asymptotics
Weyl Function
Extension Theory
Laplace-Beltrami Operator
Symmetric Operator
Asymptotic Behavior

Keywords

  • laplacian
  • self-adjoint extension
  • quasi boundary triple
  • weyl function
  • krein's formula
  • non-local boundary condition
  • schatten–von neumann class
  • singular numbers

Cite this

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A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains. / Behrndt, J.; Langer, M.; Lobanov, I.; Lotoreichik, V.; Popov, I. Yu.

In: Journal of Mathematical Analysis and Applications, Vol. 371, No. 2, 2010, p. 750-758.

Research output: Contribution to journalArticle

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AU - Popov, I. Yu.

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KW - laplacian

KW - self-adjoint extension

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KW - weyl function

KW - krein's formula

KW - non-local boundary condition

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