arXiv:1408.6022v1 [math.SP] 26 Aug 2014 Page 1 arXiv:1408.6022v1 [math.SP] 26 Aug 2014
CANONICAL SYSTEMS AND DE BRANGES SPACES R. Romanov1 This is an exposition of …

Motivated by the study of certain nonlinear wave equations (in particular, the Camassa–
Holm equation), we introduce a new class of generalized indefinite strings associated with …

We study spectral properties of two-dimensional canonical systems y′(t)= z JH (t) y (t), t∈[a,
b), where the Hamiltonian H is locally integrable on [a, b), positive semidefinite, and Weyl's …

We give a dynamical characterization of measures on the real line with finite logarithmic
integral. The general case is considered in the setting of evolution groups generated by de …

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 …

In this paper we consider two-dimensional canonical systems with discrete spectrum and
study their eigenvalue densities. We develop a formula that determines the Stieltjes …

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× …

We show that the classical Hamburger moment problem can be included in the spectral
theory of generalized indefinite strings. More precisely, we introduce the class of Krein …

Homogeneous spaces are de Branges' Hilbert spaces of entire functions with the property
that certain weighted rescaling transforms induce isometries of the space into itself. A …

We establish a sharp upper estimate for the order of a canonical system in terms of the
Hamiltonian. This upper estimate becomes an equality in the case of Krein strings. As an …