Compressions of Self-Adjoint Extensions of a Symmetric Operator and M.G. Krein’s Resolvent Formula View Full Text


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Article Info

DATE

2018-08

AUTHORS

Aad Dijksma, Heinz Langer

ABSTRACT

Let S be a symmetric operator with finite and equal defect numbers in the Hilbert space H. We study the compressions PHA~|H of the self-adjoint extensions A~ of S in some Hilbert space H~⊃H. These compressions are symmetric extensions of S in H. We characterize properties of these compressions through the corresponding parameter of A~ in M.G. Krein’s resolvent formula. If dim(H~⊖H) is finite, according to Stenger’s lemma the compression of A~ is self-adjoint. In this case we express the corresponding parameter for the compression of A~ in Krein’s formula through the parameter of the self-adjoint extension A~. More... »

PAGES

41

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00020-018-2465-3

DOI

http://dx.doi.org/10.1007/s00020-018-2465-3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1104462397


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