The resolvents of proper extensions of linear relations and finited mensional restrictions of densely defined operators
DOI:
https://doi.org/10.15407/dopovidi2018.04.003Keywords:
extension, Hilbert space, linear relation, resolventAbstract
In the terms of abstract boundary operators and corresponding Weyl functions, the resolvent set of the socalled proper extensions of closed linear relations in a Hilbert space is established, and the resolvents of the mentioned extensions are constructed. The results are applied to the case where the initial relation is the graph of the finitedimensional restriction of a closed densely defined operator.
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