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 …

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 …

In the theory of two-dimensional canonical (also called 'Hamiltonian') systems, the notion of
the Titchmarsh-Weyl coefficient associated to a Hamiltonian function plays a vital role. A …

An almost Pontryagin space can be written as the direct and orthogonal sum of a Hilbert
space, a finite-dimensional anti-Hilbert space, and a finite-dimensional neutral space. In this …

An almost Pontryagin space A is an inner product space which admits a direct and
orthogonal decomposition of the form A= A>[+˙] A≤ with a Hilbert space A> and a finite …

We define and investigate the class of symmetric and the class of semibounded de Branges
spaces of entire functions. A construction is made which assigns to each symmetric de …

Abstract An Almost Pontryagin space\left (H, ⋅, ⋅\right) admits a decomposition H= H _+ ̇+
H _-̇+ H^ ∘, where\left (H _+, ⋅, ⋅\right) and\left (H _-,-⋅, ⋅\right) are Hilbert spaces and H …

A new proof is provided for the Krein formula for generalized resolvents in the context of
symmetric operators or relations with defect numbers (1, 1) in an almost Pontryagin space …

The interest of this paper lies in the selfadjoint extensions of a symmetric relation in an
almost Pontryagin space. More in particular, in their compressed resolvents, Q-functions and …

We study S-spaces and operators therein. An S-space is a Hilbert space (S,(⋅,−)) with an
additional inner product given by [⋅,−]:=(U⋅,−), where U is a unitary operator in (S,(⋅,−)) …