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

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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
Original languageEnglish
Pages (from-to)750-758
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume371
Issue number2
DOIs
Publication statusPublished - 2010

Keywords

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

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