CaltechAUTHORS
  A Caltech Library Service

Cwikel’s theorem and the CLR inequality

Frank, Rupert L. (2014) Cwikel’s theorem and the CLR inequality. Journal of Spectral Theory, 4 (1). pp. 1-21. ISSN 1664-039X. https://resolver.caltech.edu/CaltechAUTHORS:20140530-072438434

[img]
Preview
PDF - Submitted Version
See Usage Policy.

231Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20140530-072438434

Abstract

We give a short proof of the CLR bound on the number of negative eigenvalues of Schrödinger operators. The argument, which is based on work of Rumin, leads to remarkably good constants and applies to the case of operator-valued potentials as well. Moreover, we obtain the general form of Cwikel's estimate about the singular values of operators of the form f(X)g(−i∇).


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1206.3325arXivArticle
http://www.ems-ph.org/journals/show_abstract.php?issn=1664-039X&vol=4&iss=1&rank=1PublisherArticle
http://dx.doi.org/10.4171/JST/59DOIArticle
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2014 European Mathematical Society. Received June 14, 2012. U.S. National Science Foundation grants PHY-1068285 and PHY-1347399 are acknowledged.
Funders:
Funding AgencyGrant Number
NSFPHY-1068285
NSFPHY-1347399
Subject Keywords:Cwikel inequality, trace ideals, eigenvalue inequalities, Schrödinger operators
Issue or Number:1
Classification Code:MSC (2010): 35P15, 35J10, 47B10
Record Number:CaltechAUTHORS:20140530-072438434
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140530-072438434
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:45989
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:30 May 2014 16:26
Last Modified:09 Mar 2020 13:18

Repository Staff Only: item control page