On sums of eigenvalues of elliptic operators on manifolds
| Autor: | Soufi, Ahmad El, Harrell, Evans, Ilias, Said, Stubbe, Joachim |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We use the averaged variational principle introduced in a recent article on graph spectra [7] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of Kr{\"o}ger 's bound for Neumann spectra of Laplacians on Euclidean domains [12]. Among the operators we consider are the Laplace-Beltrami operator on compact subdomains of manifolds. These estimates become more explicit and asymptotically sharp when the manifold is conformal to homogeneous spaces (here extending a result of Strichartz [21] with a simplified proof). In addition we obtain results for the Witten Laplacian on the same sorts of domains and for Schr{\"o}dinger operators with confining potentials on infinite Euclidean domains. Our bounds have the sharp asymptotic form expected from the Weyl law or classical phase-space analysis. Similarly sharp bounds for the trace of the heat kernel follow as corollaries. Comment: in Journal of Spectral Theory, 2016 |
| Databáze: | arXiv |
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