Under the mild trace-norm assumptions, we show that the eigenvalues of an arbitrary (non-
Hermitian) complex perturbation of a Jacobi matrix sequence (not necessarily real) are still …

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 …

In this paper, we obtain new results about the orthogonality measure of orthogonal
polynomials on the unit circle, through the study of unitary truncations of the corresponding …

The discrete spectrum of complex Jacobi matrices that are compact perturbations of the
discrete Laplacian is studied. The precise stabilization rate (in the sense of order) of the …

The solution of a discrete dynamical system is studied. To do so spectral properties of the
band operator, with intermediate zero diagonals, are investigated. The method of genetic …

We consider a class of random banded Hessenberg matrices with independent entries
having identical distributions along diagonals. The distributions may be different for entries …

A modification of the well-known step-by-step process for solving Nevanlinna–Pick problems
in the class of R0-functions gives rise to a linear pencil H− λJ, where H and J are Hermitian …

The definition, in previous studies, of vector Stieltjes continued fractions in connection with
spectral properties of band operators with intermediate zero diagonals, left unsolved the …

Consider the infiniteJ-fraction formula wherean∈ C {0, bn∈ C. Under very general
conditions on the coefficients an, bn, we prove that this continued fraction converges to a …

arXiv:nlin/0610010v1 [nlin.SI] 4 Oct 2006 Page 1 arXiv:nlin/0610010v1 [nlin.SI] 4 Oct 2006 On
the relation between the complex Toda and Volterra lattices Dolores Barrios Rolanıa …