Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

and Applied Analysis 3 and spectral theory for the system 1.2 . Shi studied Weyl-Titchmarsh theory and spectral theory for the system 1.2 in 33, 34 ; Clark and Gesztesy established the Weyl-Titchmarsh theory for a class of discrete Hamiltonian systems that include system 1.2 23 . Sun et al. established the GKN-theory for the system 1.2 35 . 1.3. Dynamic Equations A time scale T is an arbitrary ...

On Weyl–titchmarsh Theory for Singular Finite Difference Hamiltonian Systems

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.

Weyl-Titchmarsh theory for symplectic difference systems

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.

Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems of arbitrary order

Weyl–Titchmarsh Theory for Schrödinger Operators with Strongly Singular Potentials

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...