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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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.
|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|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||10 Feb 2006|
|Last Modified:||26 Dec 2012 08:45|
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