Sharp Spectral Asymptotics for Dirac Energy

Details Sharp Spectral Asymptotics for Dirac Energy Sharp Spectral Asymptotics for Dirac Energy

2007-08-29

arxiv.org/abs/0708.3934v1

Mathematics

Analysis of PDEs

25 pp

Scientific paper

I derive sharp semiclassical asymptotics of $\int |e_h(x,y,0)|^2\omega(x,y)
dx dy$ 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.

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