The Abstract Titchmarsh-Weyl M-function for Adjoint Operator Pairs and its Relation to the Spectrum

The Abstract Titchmarsh-weyl M-function for Adjoint Operator Pairs and Its Relation to the Spectrum

In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M -function see the same singularities as the resolvent of a certain restriction AB of the maximal operator? We obtain results showing that it is possible to describe explicitly certain spaces S and S̃ such that the resolvent bordered by projections onto these subspaces is analytic everywhere that...

The boundary control approach to the Titchmarsh-Weyl m−function. I. The response operator and the A−amplitude

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A−amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m−function associated with the Schrödinger operator H = −∂2 x + q (x) on L2 (0,∞) with Dirichlet boundary condition at x = 0.

The Evans Function and the Weyl-titchmarsh Function

We describe relations between the Evans function, a modern tool in the study of stability of traveling waves and other patterns for PDEs, and the classical Weyl-Titchmarsh function for singular Sturm-Liouville differential expressions and for matrix Hamiltonian systems. Also, we discuss a related issue of approximating eigenvalue problems on the whole line by that on finite segments.

ON A NEW ALGORITHM FOR THE COMPUTATION OF ENCLOSURES FOR THE TITCHMARSH-WEYL m-FUNCTION

Numerical computation and analysis of the Titchmarsh – Weyl m ( ) function for some simple potentials

This article is concerned with the Titchmarsh–Weyl m ( ) function for the di erential equation dy=dx+[ −q(x)]y=0. The test potential q(x) = x, for which the relevant m ( ) functions are meromorphic, having simple poles at the points = 4k + 1 and = 4k + 3, is studied in detail. We are able to calculate the m ( ) function both far from and near to these poles. The calculation is then extended to ...