J. Behrndt, M. Langer, I. Lobanov, V. Lotoreichik and I.Yu. Popov,
A remark on Schatten–von Neumann properties of resolvent differences of
generalized Robin Laplacians on bounded domains,
J. Math. Anal. Appl. 371 (2010), 750–758
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