Semi-classical measures and the Helmholtz Equation

Xue Ping Wang

Authors

Xue Ping Wang Département de Mathématiques, Laboratoire Jean Leray, CNRS-UMR 6629, Université de Nantes, 2 rue de la Houssiniere, F-44322 Nantes Cedex 03, France.

Keywords:

Mourre's method depending on a parameter, semi-classical resolvent estimates in Besov spaces, The Helmholtz equation, semi-classical measure

Abstract

In this expository article, we review and improve uniform resolvent estimates for a family of operators and show how such results can be applied to the study of the high frequency Helmboltz equation by means of semi-classical measures. For the source term concentrated near a point, we provide a complete solution to determine the semi-classical measure.