Ontology type: schema:ScholarlyArticle
2019-04
AUTHORSV. I. Mogilevskii
ABSTRACTLet A be a symmetric linear relation in the Hilbert space H with equal deficiency indices n±(A)≤∞. A self-adjoint linear relation A~⊃A in some Hilbert space H~⊃H is called an exit space extension of A; such an extension is called finite-codimensional if dim(H~⊖H)<∞. We study the compressions C(A~)=PHA~↾H of exit space extensions A~=A~∗. For a certain class of extensions A~ we parameterize the compressions C(A~) by means of abstract boundary conditions. This enables us to characterize various properties of C(A~) (in particular, self-adjointness) in terms of the parameter for A~ in the Krein formula for resolvents. We describe also the compressions of a certain class of finite-codimensional extensions. These results develop the results by A. Dijksma and H. Langer obtained for a densely defined symmetric operator A with finite and equal deficiency indices. More... »
PAGES9
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