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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. doi:10.4171/JST/59.

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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
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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.
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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
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:45989
Deposited By: Ruth Sustaita
Deposited On:30 May 2014 16:26
Last Modified:10 Nov 2021 17:19

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