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Seminario Dottorato: A pseudometric for unbounded linear operators, extension to operators defined on different open sets and an application to spectral stability estimates for eigenfunctions

Wednesday 10 March 2010 - Ermal Feleqi

ARGOMENTI: Seminari Dottorato

SEMINARIO DOTTORATO
Wednesday 10 March 2010 h. 15:00, room 2BC/30
Ermal Feleqi (Universita` di Padova - Dip. Mat.)
"A pseudometric for unbounded linear operators, extension to operators defined on different open sets and an application to spectral stability estimates for eigenfunctions"

-Abstract
A distance on closed linear subspaces/operators has long been known. It was introduced under the name of "gap" or "opening in a Hilbert space context by Krein and coworkers in the 1940s.
The first part of the talk will be of an introductory character and the main properties of the gap between subspaces/operators will be illustrated with the focus laid on spectral stability results. Next it will be shown how the notion of gap between operators can be adapted to study the spectral stability problem of a certain class of (partial) differential operators upon perturbation of the open set where they are defined on. An extension of the gap for operators defined on different open sets will be proposed and it will be estimated in terms of the geometrical vicinity or proximity of the open sets. Then, this will permit to estimate the deviation of the eigenfunctions of certain second order elliptic operators with homogeneous Dirichlet boundary conditions upon perturbation of the open set where the said operators are defined on.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva

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