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Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator
(Birkhäuser, 2013-04)
- article
In the present paper a subclass of scalar Nevanlinna functions is studied, which coincides with the class of Weyl functions associated to a nonnegative symmetric operator of defect one in a Hilbert space. This class consists ...
Infinite-dimensional perturbations, maximally nondensely defined symmetric operators, and some matrix representations
(ElsevierRoyal Netherlands Academy of Arts and Sciences (KNAW), 2012-12)
- article
The notion of a maximally nondensely defined symmetric operator or relation is introduced and characterized. The selfadjoint extensions (including the generalized Friedrichs extension) of a class of maximally nondensely ...
A Class of Sectorial Relations and the Associated Closed Forms
(Springer Nature, 2020-09-19)
- article
Let T be a closed linear relation from a Hilbert space H to a Hilbert space K and let B ∈ B(K) be selfadjoint. It will be shown that the relation T∗(I+iB)T is maximal sectorial via a matrix decomposition of B with respect ...
Boundary value problems, Weyl functions, and differential operators
(Birkhäuser, Cham, 2020)
- book
This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained ...
Factorized sectorial relations, their maximal-sectorial extensions, and form sums
(Springer, 2019-05-25)
- article
In this paper we consider sectorial operators, or more generally, sectorial relations and their maximal-sectorial extensions in a Hilbert space H. Our particular interest is in sectorial relations S, which can be expressed ...
Holomorphic operator-valued functions generated by passive selfadjoint systems
(Springer, Cham, 2019-04-09)
- bookPart
Let M be a Hilbert space. In this paper we study a class RS(m) of operator functions that are holomorphic in the domain C∖{(−∞,−1] ∪ [1,+∞)} and whose values are bounded linear operators in m . The functions in ...
Stieltjes and inverse Stieltjes holomorphic families of linear relations and their representations
(Polish Academy of Sciences, Institute of Mathematics, 2019-12-20)
- article
We study analytic and geometric properties of Stieltjes and inverse Stieltjes families defined on a separable Hilbert space and establish various minimal representations for them by means of compressed resolvents of various ...