Title: Commuting differential operators on Lie groups and spectral multipliers
Speaker: Prof. Alessio Martini Universitaet zu Kiel
Date: 27 January 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I
Let D_1,…D_n be a system of commuting, formally self-adjoint, left invariant operators on a Lie group G. Under suitable hypotheses, we show that D_1,…D_n are essentially self-adjoint on L^2(G) and admit a joint spectral resolution, and we characterize their joint L^2 spectrum as the set of eigenvalues corresponding to a class of generalized joint eigenfunctions. Moreover, in the case G is a homogeneous group and D_1,…D_n are homogeneous, we obtain L^p-boundedness results for operators of the form m(D_1,…D_n), analogous to the Mihlin-Hormander and Marcinkiewicz multiplier theorems.