Séminaire du LMPA du 14 mars 2011 à 
16h00, salle B014 :

Intervenant : Prof. Delio Mugnolo (Université Ulm, Allemagne)

Titre : Convergence of elliptic operators acting on varying Hilbert spaces.


Résumé : Convergence results for elliptic operators on Hilbert spaces
go back to Tosio Kato. In recent years, several problems have motivated
the investigation of convergence issues for elliptic operators each
acting on a different Hilbert space. If fact, in 2006 Olaf Post did
extend Kato's result to such general settings. Post has proved spectral
as well as (uniform) resolvent and semigroup convergence, in a certain
intertwined sense, in the self-adjoint case.
In this talk we present the generalisation of Post's result to the case
of  operators associated with closed forms. Convergence in the
Hilbert-Schmidt and the uniform L^p-sense are also considered. We will
briefly discuss applications of these results to systems of 3D-tubes that
are the neighbourhood of a (common) skeleton graph and, if time allows,
to families of differential operators with Wentzell-Robin boundary
conditions. This is joint work with Robin Nittka (Ulm) and Olaf Post (HU
Berlin).