On Compressions of Self-Adjoint Extensions of a Symmetric Linear Relation View Full Text


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Article Info

DATE

2019-04

AUTHORS

V. I. Mogilevskii

ABSTRACT

Let 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... »

PAGES

9

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URI

http://scigraph.springernature.com/pub.10.1007/s00020-019-2507-5

DOI

http://dx.doi.org/10.1007/s00020-019-2507-5

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https://app.dimensions.ai/details/publication/pub.1112462849


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