Short Loops and Pointwise Spectral Asymptotics

arXiv1005.0713MaRDI QIDQ6502759

Victor Ivrii

Abstract: We consider pointwise semiclassical spectral asymptotics i.e. asymptotics of $e(x,x,0)$ as $ho+0$ where $e(x,y,au)$ 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 $V=0impliesablaVe0$; (ii) Operators near boundaries.

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20)

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