18 Maggio, 2015 17:00 in punto

Seminario Matematico e Fisico di Milano

Fock-space models for evolution equations coming from quadratic differential operators

Alexandru ALEMAN, University of Lund

Sala Rappresentanza, Dipartimento di Matematica, Universita' di Milano, Via Saldini, 50

We consider evolution equations induced by an important class of quadratic differential operators which arise from the Weyl quantization of quadratic forms. This class of operators has a number of special features which makes their study quite involved. In general:
1) They are far from being selfadjoint,
2) Their eigenvectors form a minimal set with dense span, but not a Riesz basis,
3) The norm of their resolvent grows exponentially towards infinity within certain regions in the complex plane.
The aim of the talk is to present a model for such operators on Fock spaces in several complex variables, which offers a complex analysis perspective and can be used to address a number of questions about the solutions of these evolution equations.
The material is based on joint work with J. Viola.