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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