We develop Weyl–Titchmarsh theory for Schrödinger operators with strongly singular potentials such as perturbed spherical Schrödinger operators (also known as Bessel operators). It is known that in such situations one can still define a corresponding singular Weyl m-function and it was recently shown that there is also an associated spectral transformation. Here we will give a general criterion...

In this work, we establish Weyl–Titchmarsh theory for symplectic difference systems. This paper extends classical Weyl–Titchmarsh theory and provides a foundation for studying spectral theory of symplectic difference systems. 2010 Elsevier Inc. All rights reserved.

We prove a pair of uniqueness theorems for an inverse problem for an ordinary differential operator pencil of second order. The uniqueness is achieved from a discrete set of data, namely, the values at the points −n2 (n ∈ N) of (a physically appropriate generalization of) the Weyl– Titchmarsh m-function m(λ) for the problem. As a corollary, we establish a uniqueness result for a physically moti...

We provide a detailed treatment of Weyl–Titchmarsh theory for half-lattice and full-lattice CMV operators and discuss their systems of orthonormal Laurent polynomials on the unit circle, spectral functions, variants of Weyl–Titchmarsh functions, and Green’s functions. In particular, we discuss the corresponding spectral representations of half-lattice and full-lattice CMV operators.

We develop the basic theory of matrix-valued Weyl–Titchmarsh M-functions and the associated Green’s matrices for whole-line and half-line self-adjoint Hamiltonian finite difference systems with separated boundary conditions.

We explore the connections between singular Weyl–Titchmarsh theory and the single and double commutation methods. In particular, we compute the singular Weyl function of the commuted operators in terms of the original operator. We apply the results to spherical Schrödinger operators (also known as Bessel operators). We also investigate the connections with the generalized Bäcklund–Darboux trans...

The principal purpose of this note is to provide a reconstruction procedure for distributional matrix-valued potential coefficients of Schrödingertype operators on a half-line from the underlying Weyl–Titchmarsh function.

We provide a detailed treatment of Weyl–Titchmarsh theory for half-lattice and full-lattice CMV operators and discuss their systems of orthonormal Laurent polynomials on the unit circle, spectral functions, variants of Weyl–Titchmarsh functions, and Green’s functions. In particular, we discuss the corresponding spectral representations of half-lattice and full-lattice CMV operators.