2021/08/31 by Victor Ivrii, Ivrii, Victor
Computer Science · Mathematics · Physics and Astronomy · #35P20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2108.13675
openalex publication_date 2021/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish uniform (with respect to x, y) semiclassical asymptotics and estimates for the Schwartz kernel eh(x,y;τ) of spectral projector for a second order elliptic operator inside domain under microhyperbolicity (but not ξ-microhyperbolicity) assumption. 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, especially uniform ones. 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→ ∞.