On the expansion of the resolvent for elliptic boundary contact problems
| dc.creator | Krainer, Thomas | |
| dc.date | 2008-01-24 | |
| dc.date.accessioned | 2026-07-07T08:56:25Z | |
| dc.date.available | 2026-07-07T08:56:25Z | |
| dc.description | Let $A$ be an elliptic operator on a compact manifold with boundary $M$, and let $\wp : \partial\M \to Y$ be a covering map, where $Y$ is a closed manifold. Let $A_C$ be a realization of $A$ subject to a coupling condition $C$ that is elliptic with parameter in the sector $Λ$. By a coupling condition we mean a nonlocal boundary condition that respects the covering structure of the boundary. We prove that the resolvent trace $\Tr_{L^2} (A_C-λ)^{-N}$ for $N$ sufficiently large has a complete asymptotic expansion as $|λ| \to \infty$, $λ\in Λ$. In particular, the heat trace $\Tr_{L^2}e^{-tA_C}$ has a complete asymptotic expansion as $t \to 0^+$, and the $ζ$-function has a meromorphic extension to $\C$. | |
| dc.identifier | https://arxiv.org/abs/0801.3852 | |
| dc.identifier | http://arxiv.org/abs/0801.3852 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146605 | |
| dc.subject | Spectral Theory | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 58J32 | |
| dc.title | On the expansion of the resolvent for elliptic boundary contact problems | |
| dc.type | text |