Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495913 | Journal of Functional Analysis | 2005 | 12 Pages |
Abstract
Let Ej be the eigenvalues outside [-2,2] of a Jacobi matrix with an-1ââ2 and bnâ0, and μⲠthe density of the a.c. part of the spectral measure for the vector δ1. We show that if bnââ4, bn+1-bnââ2, thenâj(|Ej|-2)5/2=âand if bnââ4, bn+1-bnââ2, thenâ«-22ln(μâ²(x))(4-x2)3/2dx=-â.We also show that if an-1,bnââ3, then the above integral is finite if and only if an+1-an,bn+1-bnââ2. We prove these and other results by deriving sum rules in which the a.c. part of the spectral measure and the eigenvalues appear on opposite sides of the equation.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Andrej Zlatoš,