Pointwise Spectral Asymptotics near Singularity

arXiv2306.14213MaRDI QIDQ6441407

Victor Ivrii

Publication date: 25 June 2023

Abstract: We establish semiclassical asymptotics and estimates for the $e_h(x,x;au)$ where $e_h(x,y,au)$ is the Schwartz kernel of the spectral projector for a second order elliptic operator inside domain with power singularity in the origin. While such asymptotics for its trace $mathsf{N}_h(au)=int{e}_h(x,x,au),dx$ are well-known, the poinwise asymptotics are much less explored. Our main tools: microlocal methods, improved successive approximations and geometric optics methods.

Mathematics Subject Classification ID

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

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