Finite-dimensional Self-adjoint Extensions of a Symmetric Operator with Finite Defect and their Compressions View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2017-09-27

AUTHORS

Aad Dijksma , Heinz Langer

ABSTRACT

Let S be a symmetric operator with finite and equal defect numbers d in the Hilbert space , and with a boundary triplet . Following the method of E.A. Coddington, we describe all self-adjoint extensions of S in a Hilbert space where . The parameters in this description are matrices , where determine the compression . According to a result of W. Stenger, this compression is self-adjoint. Being a canonical self-adjoint extension of S, can be chosen as the fixed extension in M.G. Krein’s formula for the description of all generalized resolvents of S. Among other results, we describe those parameters which in Krein’s formula correspond to self-adjoint extensions of S having as their compression to . More... »

PAGES

135-163

Book

TITLE

Advances in Complex Analysis and Operator Theory

ISBN

978-3-319-62361-0
978-3-319-62362-7

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-62362-7_6

DOI

http://dx.doi.org/10.1007/978-3-319-62362-7_6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1092033156


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