Short Loops and Pointwise Spectral Asymptotics

Details Short Loops and Pointwise Spectral Asymptotics Short Loops and Pointwise Spectral Asymptotics

2010-05-05

arxiv.org/abs/1005.0713v1

Mathematics

Analysis of PDEs

23 pp, 4 figs

Scientific paper

We consider pointwise semiclassical spectral asymptotics i.e. asymptotics of
$e(x,x,0)$ as $h\to +0$ where $e(x,y,\tau)$ is the Schwartz kernel of the
spectral projector and consider two cases when schort loops give contribution
above $O(h^{1-d})$: (i) Schroedinger operator in dimensions $1,2$ as potential
$V=0\implies \nabla V\ne 0$; (ii) Operators near boundaries.

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