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Lieb–Thirring Inequalities for Jacobi Matrices

Hundertmark, Dirk and Simon, Barry (2002) Lieb–Thirring Inequalities for Jacobi Matrices. Journal of Approximation Theory, 118 (1). pp. 106-130. ISSN 0021-9045. doi:10.1006/jath.2002.3704.

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For a Jacobi matrix J on ℓ^2(Z_+) with Ju(n)=a_(n−1u)n−1)+b_nu(n)+a -nu(n+1), we prove that∑∣E∣>2(E^2−4)^(1/2)⩽∑n∣b_n∣+4∑n∣a_n−1∣. We also prove bounds on higher moments and some related results in higher dimension.

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Hundertmark, Dirk0000-0002-0643-0138
Simon, Barry0000-0003-2561-8539
Additional Information:© 2002 Elsevier Science (USA). Received 30 November 2001, Accepted 3 April 2002, Available online 3 October 2002. Supported in part by NSF Grant DMS-9707661.
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Issue or Number:1
Record Number:CaltechAUTHORS:20170512-073744584
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Official Citation:Dirk Hundertmark, Barry Simon, Lieb–Thirring Inequalities for Jacobi Matrices, Journal of Approximation Theory, Volume 118, Issue 1, 2002, Pages 106-130, ISSN 0021-9045, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77388
Deposited By: Ruth Sustaita
Deposited On:12 May 2017 23:53
Last Modified:15 Nov 2021 17:30

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