التفاصيل البيبلوغرافية
| العنوان: |
Weyl Law on Asymptotically Euclidean Manifolds |
| المؤلفون: |
Sandro Coriasco, Moritz Doll |
| بيانات النشر: |
arXiv, 2019. |
| سنة النشر: |
2019 |
| مصطلحات موضوعية: |
Nuclear and High Energy Physics, Pure mathematics, Linear operators, Logarithmic Weyl laws, Asymptotically Euclidean manifolds, Spectral zeta-function, Wave trace, Hamiltonian flow at infinity, Hamiltonian flow at infinity, 01 natural sciences, Mathematics - Spectral Theory, symbols.namesake, Mathematics - Analysis of PDEs, Euclidean geometry, FOS: Mathematics, Logarithmic Weyl laws, 0101 mathematics, Remainder, Spectral Theory (math.SP), Mathematical Physics, Eigenvalues and eigenvectors, Mathematics, Spectral zeta-function, 010102 general mathematics, Statistical and Nonlinear Physics, Asymptotically Euclidean manifolds, Manifold, Functional Analysis (math.FA), Mathematics - Functional Analysis, 010101 applied mathematics, Weyl law, Wave trace, symbols, Cotangent bundle, Hamiltonian (quantum mechanics), Analysis of PDEs (math.AP) |
| الوصف: |
We study the asymptotic behaviour of the eigenvalue counting function for self-adjoint elliptic linear operators defined through classical weighted symbols of order $(1,1)$, on an asymptotically Euclidean manifold. We first prove a two term Weyl formula, improving previously known remainder estimates. Subsequently, we show that under a geometric assumption on the Hamiltonian flow at infinity there is a refined Weyl asymptotics with three terms. The proof of the theorem uses a careful analysis of the flow behaviour in the corner component of the boundary of the double compactification of the cotangent bundle. Finally, we illustrate the results by analysing the operator $Q=(1+|x|^2)(1-\Delta)$ on $\mathbb{R}^d$.
Comment: 26 pages |
| DOI: |
10.48550/arxiv.1912.13402 |
| URL الوصول: |
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1701f19a51d51d149d00014eabcc688d |
| Rights: |
OPEN |
| رقم الانضمام: |
edsair.doi.dedup.....1701f19a51d51d149d00014eabcc688d |
| قاعدة البيانات: |
OpenAIRE |