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Sum rules for Jacobi matrices and their applications to spectral theory

Killip, Rowan and Simon, Barry (2003) Sum rules for Jacobi matrices and their applications to spectral theory. Annals of Mathematics, 158 (1). pp. 253-321. ISSN 0003-486X. http://resolver.caltech.edu/CaltechAUTHORS:KILam05

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Abstract

We discuss the proof of and systematic application of Case's sum rules for Jacobi matrices. Of special interest is a linear combination of two of his sum rules which has strictly positive terms. Among our results are a complete classification of the spectral measures of all Jacobi matrices J for which J - J(0) is Hilbert-Schmidt, and a proof of Nevai's conjecture that the Szego condition holds if J - J(0) is trace class.


Item Type:Article
Additional Information:© 2005 Princeton University. Received December 13, 2001. The first named author was supported in part by NSF grant DMS-9729992. The second named author was supported in part by NSF grant DMS-9707661.
Subject Keywords:ABSOLUTELY CONTINUOUS-SPECTRUM; DIMENSIONAL SCHRODINGER-OPERATORS; ORTHOGONAL POLYNOMIALS; DECAYING POTENTIALS; SCATTERING-THEORY; TODA LATTICE; BOUND-STATES; FINITE; INTEGRALS; NUMBER
Record Number:CaltechAUTHORS:KILam05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KILam05
Alternative URL:http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.annm/1061030450
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1653
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:10 Feb 2006
Last Modified:26 Dec 2012 08:45

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