We characterize even measures μ= wd x+ μ s on the real line R with finite entropy integral∫
R log⁡ w (t) 1+ t 2 dt>−∞ in terms of 2× 2 Hamiltonians generated by μ in the sense of the …

Based on continuity properties of the de Branges correspondence, we develop a new
approach to study the high-energy behavior of Weyl–Titchmarsh and spectral functions of 2× …

Krein–de Branges spectral theory establishes a correspondence between the class of
differential operators called canonical Hamiltonian systems and measures on the real line …

This survey article contains various aspects of the direct and inverse spectral problem for
two–dimensional Hamiltonian systems, that is, two–dimensional canonical systems of …

By a Hamiltonian, we understand a function H defined on a (possibly unbounded)
interval.(a, b), which takes real and non-negative. 2× 2-matrices as values, is locally …

We show how the change from Eulerian to Lagrangian coordinates for the two-component
Camassa–Holm system can be understood in terms of certain reparametrizations of the …

We study two-dimensional Hamiltonian systems of the form (*) where the Hamiltonian H is
locally integrable on [s-, s+) and nonnegative, and. The spectral theory of the equation …

A de Branges space B is regular if the constants belong to its space of associated functions
and is symmetric if it is isometrically invariant under the map F (z)↦ F (− z). Let KB (z, w) be …

Given a one-dimensional weighted Dirac operator we can define a spectral measure by
virtue of singular Weyl–Titchmarsh–Kodaira theory. Using the theory of de Branges spaces …

Part I of this paper deals with two-dimensional canonical systems $ y'(x)= zJH (x) y (x) $, $
x\in (a, b) $, whose Hamiltonian $ H $ is non-negative and locally integrable, and where …