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Boundary-value problems for two-dimensional canonical systems
The two-dimensional canonical systemJy′=−ℓHy where the nonnegative Hamiltonian matrix functionH(x) is trace-normed on (0, ∞) has been studied in a function-theoretic way by L. de Branges in [5]–[8].
Boundary relations and their Weyl families
The concepts of boundary relations and the corresponding Weyl families are introduced. Let S be a closed symmetric linear operator or, more generally, a closed symmetric relation in a Hilbert space
Self-Adjoint Extensions of Symmetric Subspaces
A theory of self-adjoint extensions of closed symmetric linear manifolds beyond the original space is presented. It is based on the Cayley transform of linear manifolds. Resolvent and spectral
Boundary relations and generalized resolvents of symmetric operators
The Kreĭn-Naĭmark formula provides a parametrization of all selfadjoint exit space extensions of a (not necessarily densely defined) symmetric operator in terms of maximal dissipative (in ℂ+)
A general factorization approach to the extension theory of nonnegative operators and relations
The Krein-von Neumann and the Friedrichs extensions of a nonnegative linear operator or relation (i.e., a multivalued operator) are characterized in terms of factorizations. These factorizations lead
Unitary colligations in Krein spaces and their role in the extension theory of isometries and symmetric linear relations in Hilbert spaces
Let H be a Hilbert space and let S be a closed linear relation in H, i.e., S is a * subspace of H 2 such that ScS*cH 2 (for the definition of S and other definitions see Section I). Furthermore, let
Boundary Relations, Unitary Colligations, and Functional Models
Abstract.Recently a new notion, the so-called boundary relation, has been introduced involving an analytic object, the so-called Weyl family. Weyl families and boundary relations establish a link
On the class of extremal extensions of a nonnegative operator
A nonnegative selfadjoint extension Aof a nonnegative operator A is called extremal if inf {(A)(ϕ) - f),ϕ - f) : ∈ dom A} = 0 for all ϕ ∈ dom A.A new construction of all extremal extensions of a