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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 ...
Proceedings of the Algorithmic Information Theory Conference, 16th-18th May, 2005, Vaasa
(Vaasan yliopisto, 2005)
- book
Operational calculus for rows, columns, and blocks of linear relations
(Springer, 2020-06-22)
- article
Columns and rows are operations for pairs of linear relations in Hilbert spaces, modelled on the corresponding notions of the componentwise sum and the usual sum of such pairs. The introduction of matrices whose entries ...
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 ...
Lebesgue type decompositions for nonnegative forms
(ElsevierAcademic Press, 2009-12-15)
- article
A nonnegative form t on a complex linear space is decomposed with respect to another nonnegative form w: it has a Lebesgue decomposition into an almost dominated form and a singular form. The part which is almost dominated ...
Lebesgue type decompositions and Radon–Nikodym derivatives for pairs of bounded linear operators
(Springer, 2022-09-01)
- article
For a pair of bounded linear Hilbert space operators A and B one considers the Lebesgue type decompositions of B with respect to A into an almost dominated part and a singular part, analogous to the Lebesgue decomposition ...
Generalized boundary triples, II. Some applications of generalized boundary triples and form domain invariant Nevanlinna functions
(Wiley, 2022-05-12)
- article
The paper is a continuation of Part I and contains several further results on generalized boundary triples, the corresponding Weyl functions, and applications of this technique to ordinary and partial differential operators. ...
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 ...