Spectral problems for generalized Jacobi matrices

Two modified Jacobi methods for M-matrices

Spectral averaging techniques for Jacobi matrices

Spectral averaging techniques for one-dimensional discrete Schrödinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the density of the averaged spectral measures. These Wegner type estimates are used to analyze stability properties for the spectral types of Jacobi matrices under ...

A spectral equivalence for Jacobi matrices

We use the classical results of Baxter and Gollinski-Ibragimov to prove a new spectral equivalence for Jacobi matrices on l(N). In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences, and find necessary and sufficient conditions on the spectral measure such that ∑ ∞ k=n bk and ∑ ∞ k=n (a k − 1) lie in l 1 ∩ l .

On Generalized Sum Rules for Jacobi Matrices

This work is in a stream (see e.g. [4], [8], [10], [11], [7]) initiated by a paper of Killip and Simon [9], an earlier paper [5] also should be mentioned here. Using methods of Functional Analysis and the classical Szegö Theorem we prove sum rule identities in a very general form. Then, we apply the result to obtain new asymptotics for orthonormal polynomials.

On a Spectral Property of Jacobi Matrices

Let J be a Jacobi matrix with elements bk on the main diagonal and elements ak on the auxiliary ones. We suppose that J is a compact perturbation of the free Jacobi matrix. In this case the essential spectrum of J coincides with [−2, 2], and its discrete spectrum is a union of two sequences {xj }, x + j > 2, x − j < −2, tending to ±2. We denote sequences {ak+1 − ak} and {ak+1 + ak−1 − 2ak} by ∂...