The selfadjoint extensions of a closed linear relation R from a Hilbert space h1 to a Hilbert space h2 are considered in the Hilbert space <$Eh sub 1 ~symbol е~h sub 2> that contains the graph of R. They will be described by <$E2~times~2> blocks of linear relations and by means of boundary triplets associated with a closed symmetric relation S in <$Eh sub 1 ~symbol е~h sub 2> that is induced by R. Such a relation is characterized by the orthogonality property dom S <$Esymbol <94>> 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 dom A <$Esymbol <94>> 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.

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