Compressions of Self-Adjoint Extensions ofa Symmetric Operator and M.G. Krein’sResolvent Formula

Dijksma, Aad; Langer, Heinz

doi:10.1007/s00020-018-2465-3

Record link:

https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:3-5236
http://hdl.handle.net/20.500.12708/577

Title:

Compressions of Self-Adjoint Extensions ofa Symmetric Operator and M.G. Krein’sResolvent Formula

Citation:

Dijksma, A., & Langer, H. (2018). Compressions of Self-Adjoint Extensions ofa Symmetric Operator and M.G. Krein’sResolvent Formula. Integral Equations and Operator Theory. https://doi.org/10.1007/s00020-018-2465-3

Publisher DOI:

10.1007/s00020-018-2465-3

CatalogPlus:

AC15324301

Publication Type:

Article - Original Research Article

Language:

English

Authors:

Dijksma, Aad
Langer, Heinz

Organisational Unit:

E101 - Institut für Analysis und Scientific Computing

Journal:

Integral Equations and Operator Theory

ISSN:

0378-620X

Date (published):

2018

Publisher:

Birkhäuser

Peer reviewed:

Yes

Keywords:

Hilbert space; Symmetric and self-adjoint operators; Self-adjoint extension; Compression Generalized resolvent; Krein’s resolvent formula; Q-function

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˜.

License:

CC BY 4.0