H. de Snoo

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Articles: 4

Selfadjoint extensions of relations whose domain and range are orthogonal

S. Hassi, J.-Ph. Labrousse, H.S.V. de Snoo

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 26 (2020), no. 1, 39-62

The selfadjoint extensions of a closed linear relation $R$ from a Hilbert space $\mathfrak H_1$ to a Hilbert space $\mathfrak H_2$ are considered in the Hilbert space $\mathfrak H_1\oplus\mathfrak H_2$ that contains the graph of $R$. They will be described by $2 \times 2$ blocks of linear relations and by means of boundary triplets associated with a closed symmetric relation $S$ in $\mathfrak H_1 \oplus \mathfrak H_2$ that is induced by $R$. Such a relation is characterized by the orthogonality property ${\rm dom\,} S \perp {\rm ran\,} S$ and it is nonnegative. All nonnegative selfadjoint extensions $A$, in particular the Friedrichs and Krein-von Neumann extensions, are parametrized via an explicit block formula. In particular, it is shown that $A$ belongs to the class of extremal extensions of $S$ if and only if ${\rm dom\,} A \perp {\rm ran\,} A$. In addition, using asymptotic properties of an associated Weyl function, it is shown that there is a natural correspondence between semibounded selfadjoint extensions of $S$ and semibounded parameters describing them if and only if the operator part of $R$ is bounded.

Operator models associated with singular perturbations

Henk de Snoo, Vladimir Derkach, Seppo Hassi

Methods Funct. Anal. Topology 7 (2001), no. 3, 1-21

Generalized resolvents of symmetric operators and admissibility

H. S. V. de Snoo, V. A. Derkach, S. Hassi, M. M. Malamud

Methods Funct. Anal. Topology 6 (2000), no. 3, 24-55

Operator models associated with Kac subclasses of generalized Nevanlinna functions

Henk de Snoo, Vladimir Derkach, Seppo Hassi

Methods Funct. Anal. Topology 5 (1999), no. 1, 65-87

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