|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
The Friedrichs extension of the energy Laplacian | | Palle E. T. Jorgensen
; Erin P. J. Pearse
; | | Date: |
30 Mar 2011 | | Abstract: | We study Laplace operators on infinite networks $(G,c)$, and their
self-adjoint extensions. We consider the Laplacian $Delta$ as on operator on
$ell^2(G)$ and as an operator on the Hilbert space $mathcal{H}_mathcal{E}$
of finite energy functions on $G$, focusing on the case when $Delta$ is
unbounded. It is known that $Delta$ is essentially self-adjoint on its natural
domain in $ell^2(G)$, but that it is emph{not} essentially self-adjoint on
its natural domain in $mathcal{H}_mathcal{E}$. We characterize the Friedrichs
extension of the energy Laplacian on $mathcal{H}_mathcal{E}$ in terms of the
Laplacian on $ell^2(G)$ and show that the spectral measures of the Laplacian
on $ell^2(G)$ and the Friedrichs extension on $mathcal{H}_mathcal{E}$ are
mutually absolutely continuous with Radon-Nikodym derivative $lambda$ (the
spectral parameter). We give a formula for its computation and derive a number
of spectral-theoretic conclusions, including applications to the effective
resistance on $(G,c)$. | | Source: | arXiv, 1103.5792 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER