Semiclassical Eigenfunction Estimates

Semiclassical Eigenfunction Estimates - Melissa Tacy

Melissa Tacy
Institute for Advanced Study
October 29, 2010


Concentration phenomena for Laplacian eigenfunctions can be studied by obtaining estimates for their $L^{p}$ growth. By considering eigenfunctions as quasimodes (approximate eigenfunctions) within the semiclassical framework we can extend such estimates to a more general class of semiclassical operators. This talk will focus on $L^{p}$ estimates for quasimodes restricted to hypersurfaces and the links between such estimates and properties of classical flow.