The two-dimensional canonical system Jy′=− ℓ Hy where the nonnegative Hamiltonian
matrix function H (x) is trace-normed on (0,∞) has been studied in a function-theoretic way …

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 …

This paper solves explicitly the direct spectral problem of canonical differential systems for a
special class of potentials. For a potential from this class the corresponding spectral function …

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 …

An inverse problem for a class of canonical systems having Hamiltonians of determinant one -
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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 …

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 …

We consider a singular two-dimensional canonical system Jy'=− zHy on [0, L) such that at L
Weyl's limit point case holds. Here H is a real and nonnegative definite matrix function, the …

In this note, we study inverse spectral problems for canonical Hamiltonian systems, which
encompass a broad class of second‐order differential equations on a half‐line. Our goal is …

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 …