2021/07/10 by Victor Ivrii, Ivrii, Victor
Mathematics · Physics and Astronomy · #35P20 #FOS: Mathematics #Quantum chaos and dynamical systems #Scientific Research and Discoveries #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2107.04807
openalex publication_date 2021/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish semiclassical asymptotics and estimates for the Schwartz kernel eh(x,y;τ) of spectral projector for a second order elliptic operator on the manifold with a boundary. While such asymptotics for its restriction to the diagonal eh(x,x,τ) and, especially, for its trace Nh(τ)= ∫ eh(x,x,τ) dx are well-known, the out-of-diagonal asymptotics are much less explored. Our main tools: microlocal methods, improved successive approximations and geometric optics methods. Our results would also lead to classical asymptotics of eh(x,y,τ) for fixed h (say, h=1) and τ→ ∞.