Journal article
Symmetric Pairs and Self-Adjoint Extensions of Operators, with Applications to Energy Networks
Complex analysis and operator theory, Vol.10(7), pp.1535-1550
10/01/2016
DOI: 10.1007/s11785-015-0522-3
Abstract
We provide a streamlined construction of the Friedrichs extension of a densely-defined self-adjoint and semibounded operator A on a Hilbert space , by means of a symmetric pair of operators. A symmetric pair is comprised of densely defined operators and which are compatible in a certain sense. With the appropriate definitions of and J in terms of A and , we show that is the Friedrichs extension of A. Furthermore, we use related ideas (including the notion of unbounded containment) to construct a generalization of the construction of the Krein extension of A as laid out in a previous paper of the authors. These results are applied to the study of the graph Laplacian on infinite networks, in relation to the Hilbert spaces and (the energy space).
Details
- Title: Subtitle
- Symmetric Pairs and Self-Adjoint Extensions of Operators, with Applications to Energy Networks
- Creators
- Palle E. T Jorgensen - University of IowaErin P. J Pearse - California Polytechnic State University
- Resource Type
- Journal article
- Publication Details
- Complex analysis and operator theory, Vol.10(7), pp.1535-1550
- DOI
- 10.1007/s11785-015-0522-3
- ISSN
- 1661-8254
- eISSN
- 1661-8262
- Publisher
- SPRINGER BASEL AG
- Number of pages
- 16
- Language
- English
- Date published
- 10/01/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9984241045502771
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