Article ID Journal Published Year Pages File Type
9495913 Journal of Functional Analysis 2005 12 Pages PDF
Abstract
Let Ej be the eigenvalues outside [-2,2] of a Jacobi matrix with an-1∈ℓ2 and bn→0, and μ′ the density of the a.c. part of the spectral measure for the vector δ1. We show that if bn∉ℓ4, bn+1-bn∈ℓ2, then∑j(|Ej|-2)5/2=∞and if bn∈ℓ4, bn+1-bn∉ℓ2, then∫-22ln(μ′(x))(4-x2)3/2dx=-∞.We also show that if an-1,bn∈ℓ3, then the above integral is finite if and only if an+1-an,bn+1-bn∈ℓ2. 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.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
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