Sum rules for Jacobi matrices and their applications to spectral theory

Rowan Killip, Barry Simon

Type: Article

Publication Date: 2003-07-01

Citations: 288

DOI: https://doi.org/10.4007/annals.2003.158.253

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 Szegő condition holds if J -J 0 is trace class.

Locations

arXiv (Cornell University) - View - PDF
CaltechAUTHORS (California Institute of Technology) - View - PDF
Annals of Mathematics - View - PDF

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Action	Title	Year	Authors
+	Orthogonal Polynomials, Recurrences, Jacobi Matrices, and Measures	1992	Paul Nevai
+ PDF Chat	Jacobi Operators and Completely Integrable Nonlinear Lattices	1999	Gerald Teschl
+	Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results	1998	Michael Christ Alexander Kiselev
+	Analytic Theory of Continued Fractions	1967	H. S. Wall
+	Introduction to the theory of linear nonselfadjoint operators	1969	M. Г. Крейн Israel Gohberg
+	The statistical mechanics of lattice gases	1993	Barry Simon
+	Methods of Modern Mathematical Physics	1972	Michael C. Reed Barry Simon
+	Real and Complex Analysis.	1987	G. A. Garreau Walter Rudin
+	Trace Ideals and Their Applications	2010	Barry Simon
+	Linear Transformations in Hilbert Space and Their Applications to Analysis	1932	Margaret E. Stone