We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line SchrÃ¶dinger operators on [a,âˆž), a âˆˆ R, with a regular finite end point a and the case ofâ€¦ (More)

We provide a detailed treatment of Weylâ€“Titchmarsh theory for half-lattice and full-lattice CMV operators and discuss their systems of orthonormal Laurent polynomials on the unit circle, spectralâ€¦ (More)

We study various spectral theoretic aspects of nonselfadjoint operators. Specifically, we consider a class of factorable nonselfadjoint perturbations of a given unperturbed nonselfadjoint operatorâ€¦ (More)

We prove a general Borg-type result for reflectionless unitary CMV operators U associated with orthogonal polynomials on the unit circle. The spectrum of U is assumed to be a connected arc on theâ€¦ (More)

We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the SchrÃ¶dinger operator on a half-line to aâ€¦ (More)

We prove that Jacobi, CMV, and SchrÃ¶dinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discreteâ€¦ (More)

Let e âŠ‚ R be a finite union of + 1 disjoint closed intervals, and denote by Ï‰j the harmonic measure of the j left-most bands. The frequency module for e is the set of all integral combinations of Ï‰1,â€¦ (More)

We provide a concise, yet fairly complete discussion of the concept of essential closures of subsets of the real axis and their intimate connection with the topological support of absolutelyâ€¦ (More)

Let e âŠ‚ R be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a SzegÅ‘ condition isâ€¦ (More)

The aim of this paper is twofold: On one hand we discuss an abstract approach to symmetrized Fredholm perturbation determinants and an associated trace formula for a pair of operators ofâ€¦ (More)