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Quasi boundary triples and semi-bounded self-adjoint extensions

Part of: Partial differential operators Special classes of linear operators Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  28 June 2017

Jussi Behrndt ,
Matthias Langer ,
Vladimir Lotoreichik  and
Jonathan Rohleder
Jussi Behrndt
Affiliation:
Technische Universität Graz, Institut für Numerische Mathematik, Steyrergasse 30, 8010 Graz, Austria (behrndt@tugraz.at)
Matthias Langer
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK (m.langer@strath.ac.uk)
Vladimir Lotoreichik
Affiliation:
Department of Theoretical Physics, Nuclear Physics Institute ASCR, 250 68 Řež near Prague, Czech Republic (lotoreichik@ujf.cas.cz)
Jonathan Rohleder
Affiliation:
Technische Universität Graz, Institut für Numerische Mathematik, Steyrergasse 30, 8010 Graz, Austria
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In this note semi-bounded self-adjoint extensions of symmetric operators are investigated with the help of the abstract notion of quasi boundary triples and their Weyl functions. The main purpose is to provide new sufficient conditions on the parameters in the boundary space to induce self-adjoint realizations, and to relate the decay of the Weyl function to estimates on the lower bound of the spectrum. The abstract results are illustrated with uniformly elliptic second-order partial differential equations on domains with non-compact boundaries.

Keywords

semi-bounded operatorboundary tripleWeyl functionelliptic differential operatorDirichlet–Neumann map

MSC classification

Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds 47F05: Partial differential operators (should also be assigned at least one other classification number in section 47) 35P05: General topics in linear spectral theory 47B25: Symmetric and selfadjoint operators (unbounded)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 5 , October 2017 , pp. 895 - 916
Copyright
Copyright © Royal Society of Edinburgh 2017