Spectral Theory Seminar 

22/04/2004, 10:30 — 11:30 — Room P4.35, Mathematics Building
Jorge Silva, Instituto Superior Técnico

A review of methods for obtaining approximate fundamental solutions to linear PDEs: Pseudodifferential Operators and Fourier Integral Operators

We will give a fast overview of the Fourier Analysis methods for obtaining parametrices for linear partial differential operators with non-constant coefficients. These are approximate fundamental solutions in the sense that, modulo smooth functions, they produce the Dirac measure when acted by the operator. These methods have become fundamental tools for the microlocal analysis of distributions, accurate control of singularities of solutions for linear PDEs with variable coefficients and spectral analysis of the same operators.