Sharp Spectral Asymptotics for Dirac Energy

Abstract

I derive sharp semiclassical asymptotics of $\int |e_h(x,y,0){|}^2\omega (x,y)dxdy$ where $e_h(x,y,\tau )$ is the Schwartz kernel of the spectral projector and $\omega (x,y)$ is singular as $x=y$. I also consider asymptotics of more general expressions.

25 pp