Two-term spectral asymptotics for the Dirichlet pseudo-relativistic kinetic energy operator on a bounded domain
| Autor: | Sebastian Gottwald |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Physics
Nuclear and High Energy Physics Series (mathematics) 010102 general mathematics G.1.8 Boundary (topology) Statistical and Nonlinear Physics Mathematics::Spectral Theory 01 natural sciences Dirichlet distribution Combinatorics Mathematics - Spectral Theory 010104 statistics & probability symbols.namesake Bounded function Dirichlet boundary condition Domain (ring theory) symbols FOS: Mathematics 35P20 47G30 Asymptotic formula 0101 mathematics Asymptotic expansion Spectral Theory (math.SP) Mathematical Physics |
| Popis: | Continuing the series of works following Weyl's one-term asymptotic formula for the counting function $N(\lambda)=\sum_{n=1}^\infty(\lambda_n{-}\lambda)_-$ of the eigenvalues of the Dirichlet Laplacian and the much later found two-term expansion on domains with highly regular boundary by Ivrii and Melrose, we prove a two-term asymptotic expansion of the $N$-th Ces\`aro mean of the eigenvalues of $\sqrt{-\Delta + m^2} - m$ for $m>0$ with Dirichlet boundary condition on a bounded domain $\Omega\subset\mathbb R^d$ for $d\geq 2$, extending a result by Frank and Geisinger for the fractional Laplacian ($m=0$) and improving upon the small-time asymptotics of the heat trace $Z(t) = \sum_{n=1}^\infty e^{-t \lambda_n}$ by Ba\~nuelos et al. and Park and Song. Comment: Ann. Henri Poincar\'e (2018) |
| Databáze: | OpenAIRE |
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