The relation between the counting function N(lambda) and the heat kernel K(t)
| dc.creator | Dai, Wu-Sheng | |
| dc.creator | Xie, Mi | |
| dc.date | 2007-03-28 | |
| dc.date | 2008-02-17 | |
| dc.date.accessioned | 2026-07-07T09:21:02Z | |
| dc.date.available | 2026-07-07T09:21:02Z | |
| dc.description | For a given spectrum {lambda_{n}} of the Laplace operator on a Riemannian manifold, in this paper, we present a relation between the counting function N(lambda), the number of eigenvalues (with multiplicity) smaller than λ, and the heat kernel K(t), defined by K(t)=\sum_{n}e^{-lambda_{n}t}. Moreover, we also give an asymptotic formula for N(λ) and discuss when lambda \to \infty in what cases N(lambda)=K(1/lambda). | |
| dc.description | 5 pages, no figure | |
| dc.identifier | https://arxiv.org/abs/math/0703847 | |
| dc.identifier | http://arxiv.org/abs/math/0703847 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154886 | |
| dc.subject | Spectral Theory | |
| dc.title | The relation between the counting function N(lambda) and the heat kernel K(t) | |
| dc.type | text |