Let the function Q be holomorphic in he upper half plane ℂ+ and such that Im Q (z≥ 0 and
Im zQ (z)≥ 0 if z ε ℂ+. A basic result of MG Krein states that these functions Q are the …

We continue the study of a generalization of L. de Branges's theory of Hilbert spaces of
entire functions to the Pontryagin space setting. In this-second-part we investigate isometric …

The subject of this survey is to review the basics of Louis de Branges' theory of Hilbert
spaces of entire functions, and to present results bringing together the notions of de Branges …

A canonical differential equation is a system y′= zJHy with a real, nonnegative and locally
integrable 2× 2-matrix valued function H. The theory of a canonical system is closely related …

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 …

Oscillation theory locates the spectrum of a differential equation by counting the zeros of its
solutions. We present a version of this theory for canonical systems Ju0 D zH u and then use …

We study the minimum of the essential spectrum of canonical systems J u′=− z H u. Our
results can be described as a generalized and more quantitative version of the …

We investigate the structure of a maximal chain of matrix functions whose Weyl coefficient
belongs to N _ κ^+. It is shown that its singularities must be of a very particular type. As an …

We consider a Hamiltonian system of the form y (x)= jh (x) y (x), with a locally integrable and
nonnegative 2 x 2-matrix-valued Hamiltonian (H). I n the literature dealing with the operator …

We present two inverse spectral relations for canonical differential equations Jy′(x)=-zH (x)
y (x), x∈[0, L): Denote by QH the Titchmarsh–Weyl coefficient associated with this equation …