Spectral Calculus for Schrödinger Operators in One and Three Dimensions

Presenters/Authors

Shijun Zheng, Georgia Southern UniversityFollow

Document Type

Presentation

Presentation Date

11-6-2006

Abstract or Description

In this talk we consider Hormander type spectral multiplier problem for Schrödinger operator with a critical potential in one and three dimensions. It is shown that the multiplier operator is bounded on L^p, Besov spaces and Triebel-Lizorkin spaces under the same sharp condition. We then derive Strichartz estimates for the corresponding wave equations. Our work is partially motivated by the standing wave problem for the quintic wave equation in 3+1 spacetime dimensions.

Sponsorship/Conference/Institution

Analysis and Partioal Differential Equations Seminar

Location

Baltimore, MD

Recommended Citation

Zheng, Shijun. 2006. "Spectral Calculus for Schrödinger Operators in One and Three Dimensions." Department of Mathematical Sciences Faculty Presentations. Presentation 424.
https://digitalcommons.georgiasouthern.edu/math-sci-facpres/424