March 29

Avy Soffer (Rutgers University)

Monotonic Local decay estimates

A new class of Propagation estimates for the wave and Schroediner equation,
based on analytic microlocalization is described.
In particular, it leads to decay estimates which are monotonic in time,
with no higher order (Quantum) corrections.
This approach is then used to prove some optimal, and improved decay
estimates for the wave equation on Schwarzschild manifolds, and provides
some alternative to Mourre Method at thresholds and high energies; it
allows the use of L^2 bounded multipliers instead of Morawetz type first
order operators.