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Title: Pointwise Spectral Asymptotics near Singularity

Abstract:

In this talk we establish semiclassical asymptotics and estimates for the $e_h(x,x,\tau)$ where

$e_h(x,y,\tau)$ is the Schwartz kernel of the spectral projector for a second order elliptic operator inside domain with the power singularity in the origin. While such asymptotics for its trace $\N_h(\tau)= \int e_h(x,x,\tau)\,dx$ are well-known, the poinwise asymptotics are much less explored.

Our main tools: microlocal methods, improved successive approximations and geometric optics methods.

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The will take place next Thursday, November 9, at the CRM, and may be of interest to the seminar audience.

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