16 nov 2005
Abstract.
Seminario di Analisi Analysis seminar
when: Wednesady, November 16, at 16 pm
where: Dipartimento di Matematica, Sala Riunioni
speaker: Piero D'Ancona (Università di Roma I)
title: The wave operator with variable coefficients in dimension 1
abstract: The wave operator intertwines the perturbed Schroedinger operator $-\Delta+V(x)$ with the free operator $-\Delta$. This allows to extend many results from the free to the perturbed case. In particular, by proving the $L^p$ boundeness of the wave operator one gets as immediate consequences the decay estimates for a number of evolution equations with variable coefficients (waves, heat, Schroedinger). Recently, in a joint work with L. Fanelli we have obtained new results about the $L^p$ boundeness of the one-dimensional wave operator with variable coeffcients, improving previous results of Artbazar-Yajima and Weder. We believe that our results are optimal from the point of view of the regularity of coefficients.