29/04/2004, 10:30 — 11:30 — Room P4.35, Mathematics Building Jorge Silva, Instituto Superior Técnico
Fourier Integral Operators: the construction of parametrices for
strictly hyperbolic Cauchy problems
After having seen how to construct approximate fundamental
solutions for elliptic linear PDEs, in the first lecture of this
series, we will now review the construction of similar approximate
solutions, this time for the Cauchy problem in hyperbolic problems,
using Fourier Integral Operators. These operators can be seen as a
generalization of pseudo-differential operators, and bring into the
picture a strong symplectic geometry component, related to the
hamiltonian evolution in phase-space: the cotangent bundle of space
points and Fourier frequencies.