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

Behrndt, J. and Langer, M. and Lobanov, I. and Lotoreichik, V. and Popov, I. Yu. (2010) A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains. Journal of Mathematical Analysis and Applications, 371 (2). pp. 750-758. ISSN 0022-247X

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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