Orthogonal polynomials on the real line (OPRL) were developed in the nineteenth century
and orthogonal polynomials on the unit circle (OPUC) were initially developed around 1920 …

Building on work on Miura's transformation by Kappeler, Perry, Shubin, and Topalov, we
develop a detailed spectral theoretic treatment of Schrödinger operators with matrix-valued …

Recently, Bohner and Sun [9] introduced basic elements of a Weyl–Titchmarsh theory into
the study of discrete symplectic systems. We extend this development through the …

In this paper we develop the Weyl–Titchmarsh theory for discrete symplectic systems with
general linear dependence on the spectral parameter. We generalize and complete several …

A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with
rectangular matrix potentials. The notion of the Weyl function is introduced and direct and …

Abstract We consider (2× 2)-Hamiltonian systems of the form y'(x)= zJH (x) y (x), x∊[s−, s+). If
a system of this form is in the limit point case, an analytic function is associated with it …

In this paper we characterize the definiteness of the discrete symplectic system, study a
nonhomogeneous discrete symplectic system, and introduce the minimal and maximal …

Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The
corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non …

It is well known that an operator-valued function $\Theta $ from the Schur class ${\bf
S}(\mathfrak M,\mathfrak N) $, where $\mathfrak M $ and $\mathfrak N $ are separable …

Discrete Dirac type self-adjoint system is equivalent to the block Szeg\" o recurrence.
Representation of the fundamental solution is obtained, inverse problems on the interval …