A new inverse three spectra theorem for Jacobi matrices

A Strong Szegő Theorem for Jacobi Matrices

We use a classical result of Gollinski and Ibragimov to prove an analog of the strong Szegő theorem for Jacobi matrices on l2(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 2 k − 1) lie in l2 1, the linearly-weighted l2 space.

On an inverse eigenproblem for Jacobi matrices

Recently Xu 13] proposed a new algorithm for computing a Jacobi matrix of order 2n with a given n n leading principal submatrix and with 2n prescribed eigenvalues that satisfy certain conditions. We compare this algorithm to a scheme proposed by Boley and Golub 2], and discuss a generalization that allows the conditions on the prescribed eigenvalues to be relaxed.

Titchmarsh theorem for Jacobi Dini-Lipshitz functions

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

On Rakhmanov’s Theorem for Jacobi Matrices

We prove Rakhmanov’s theorem for Jacobi matrices without the additional assumption that the number of bound states is finite. This result solves one of Nevai’s open problems. Consider a measure dμ with bounded support in R. Assume that it has infinitely many growth points. Let {pk} (k = 0, 1, . . .) be the system of polynomials orthonormal with respect to that measure, i.e., ∞ ∫ −∞ pk(x)pm(x)dμ...

Two modified Jacobi methods for M-matrices