Add to ORKGPart I of this paper deals with two-dimensional canonical systems $y'(x)=yJH(x)y(x)$, $x\in(a,b)$, whose Hamiltonian $H$ is non-negative and locally integrable, and where Weyl's limit point case takes place at both endpoints $a$ and $b$. We investigate a class of such systems defined by growth restrictions on H towards a. For example, Hamiltonians on $(0,\infty)$ of the form $H(x):=\begin{pmatrix}x^{-\alpha}&0\\ 0&1\end{pmatrix}$ where $\alpha<2$ are included in this class. We develop a direct and inverse spectral theory parallel to the theory of Weyl and de Branges for systems in the limit circle case at $a$. Our approach proceeds via - and is bound to - Pontryagin space theory. It relies on spectral theory and operator models in such spac...
Recently, a generalization to the Pontryagin space setting of the notion of canonical (Hamiltonian) ...
The main purpose of this paper is to develop Titchmarsh- Weyl theory of canonical systems. To this e...
In this paper, we extend the Remling’s Theorem on canonical systems that the ω limit points of the H...
This survey article contains various aspects of the direct and inverse spectral problem for twodimen...
For a two-dimensional canonical system $y'(t)=zJH(t)y(t)$ on some interval $(a,b)$ whose Hamiltonian...
We study two-dimensional Hamiltonian systems of the form (•) y'(x) = zJH(x)y(x); x ∈ [s-; s+), where...
The two-dimensional Hamiltonian system (*) y'(x)=zJH(x)y(x), x∈(a,b), where the Hamiltonian H take...
For a two-dimensional canonical system y'(t)=zJH(t)y(t) on the half-line (0, ∞) whose Hamiltonian H ...
In this note we study inverse spectral problems for canonical Hamiltonian systems, which encompass a...
We consider (2×2)-Hamiltonian systems of the form $y'(x) = zJH(x)y(x)$, $x \in [s−, s+)$. If a syste...
AbstractThis paper is concerned with establishing the Weyl–Titchmarsh theory for a class of discrete...
Abstract. We present two inverse spectral relations for canonical differential equations Jy′(x) = −...
We investigate two-dimensional canonical systems $y'=zJHy$ on an interval, with positive semi-defini...
AbstractA linear Hamiltonian system Jy′ = (λA + B) y is considered on an open interval (a, b), where...
We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time sc...
Recently, a generalization to the Pontryagin space setting of the notion of canonical (Hamiltonian) ...
The main purpose of this paper is to develop Titchmarsh- Weyl theory of canonical systems. To this e...
In this paper, we extend the Remling’s Theorem on canonical systems that the ω limit points of the H...
This survey article contains various aspects of the direct and inverse spectral problem for twodimen...
For a two-dimensional canonical system $y'(t)=zJH(t)y(t)$ on some interval $(a,b)$ whose Hamiltonian...
We study two-dimensional Hamiltonian systems of the form (•) y'(x) = zJH(x)y(x); x ∈ [s-; s+), where...
The two-dimensional Hamiltonian system (*) y'(x)=zJH(x)y(x), x∈(a,b), where the Hamiltonian H take...
For a two-dimensional canonical system y'(t)=zJH(t)y(t) on the half-line (0, ∞) whose Hamiltonian H ...
In this note we study inverse spectral problems for canonical Hamiltonian systems, which encompass a...
We consider (2×2)-Hamiltonian systems of the form $y'(x) = zJH(x)y(x)$, $x \in [s−, s+)$. If a syste...
AbstractThis paper is concerned with establishing the Weyl–Titchmarsh theory for a class of discrete...
Abstract. We present two inverse spectral relations for canonical differential equations Jy′(x) = −...
We investigate two-dimensional canonical systems $y'=zJHy$ on an interval, with positive semi-defini...
AbstractA linear Hamiltonian system Jy′ = (λA + B) y is considered on an open interval (a, b), where...
We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time sc...
Recently, a generalization to the Pontryagin space setting of the notion of canonical (Hamiltonian) ...
The main purpose of this paper is to develop Titchmarsh- Weyl theory of canonical systems. To this e...
In this paper, we extend the Remling’s Theorem on canonical systems that the ω limit points of the H...