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.