## Spectral multipliers for Schroedinger operators in one and three dimensions

- Sept. 27, 2006
- 3:30 p.m.
- LeConte 312

## Abstract

In this talk we consider spectral multiplier problem for Schroedinger operator with a critical potential in one and three dimensions. It is shown that the multiplier operator is bounded on Lp, Besov spaces and Triebel-Lizorkin spaces under the same sharp condition. Moreover, we establish Strichartz estimates in measuring the regularity of solutions to the corresponding wave equation. Our work is partially motivated by the standing wave problem for the quintic wave equation.