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A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains |
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| Authors: | Jussi Behrndt Matthias Langer |
| Affiliation: | a Technische Universität Berlin, Institut für Mathematik, MA 6-4, Straße des 17. Juni 136, 10623 Berlin, Germany b Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, United Kingdom c Department of Mathematics, St. Petersburg State University of Information Technologies, Mechanics and Optics, Kronverkskiy, 49, St. Petersburg, Russia |
| 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 |
| 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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