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Published September 2002 | public
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Lieb–Thirring Inequalities for Jacobi Matrices

Hundertmark, Dirk ORCID icon
Simon, Barry ORCID icon
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Abstract

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.

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.

Additional details

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Created:
August 19, 2023
Modified:
October 25, 2023