Mathematics – Spectral Theory
Scientific paper
2009-11-12
J. Math. Anal. Appl. 371(2) 2010, 750-758
Mathematics
Spectral Theory
Scientific paper
In this note we investigate the asymptotic behaviour of the $s$-numbers of the resolvent difference of two generalized self-adjoint, maximal dissipative or maximal accumulative Robin Laplacians on a bounded domain $\Omega$ with smooth boundary $\partial\Omega$. 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 $\partial\Omega$. It will be shown that the resolvent difference of two generalized Robin Laplacians belongs to the Schatten-von Neumann class of any order $p$ for which $p>(dim\Omega-1)/3$. Moreover, we also give a simple sufficient condition for the resolvent difference of two generalized Robin Laplacians to belong to a Schatten-von Neumann class of arbitrary small order. Our results extend and complement classical theorems due to M.Sh.Birman on Schatten-von Neumann properties of the resolvent differences of Dirichlet, Neumann and self-adjoint Robin Laplacians.
Behrndt Jussi
Langer Matthias
Lobanov Igor
Lotoreichik Vladimir
Popov I. I.
No associations
LandOfFree
A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-151076