Lieb–Thirring Bounds for Complex Jacobi Matrices

Two modified Jacobi methods for M-matrices

Complex Jacobi Matrices

Complex Jacobi matrices play an important role in the study of asymptotics and zero distribution of Formal Orthogonal Polynomials (FOPs). The latter are essential tools in several elds of Numerical Analysis, for instance in the context of iterative methods for solving large systems of linear equations, or in the study of Pad e approximation and Jacobi continued fractions. In this paper we prese...

Upper bounds on wavepacket spreading for random Jacobi matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argum...

On the determinacy of complex Jacobi matrices

The aim of this paper is to explore to which extend the theory of the Hamburger moment problem for real Jacobi matrices generalizes to the case of complex Jacobi matrices. In particular, we characterize the indeterminacy in terms of uniqueness of closed extensions of Jacobi matrices, and discuss the link to the growth of the smallest singular values of the underlying Hankel matrices. As a bypro...

DETERMINACY OF COMPLEX JACOBI MATRICES 21 Introdu