Quasi boundary triples and semibounded self-adjoint extensions

Jussi Behrndt; Matthias Langer; Vladimir Lotoreichik; Jonathan Rohleder

doi:10.1017/S0308210516000421

Quasi boundary triples and semibounded self-adjoint extensions

Jussi Behrndt^*, Matthias Langer, Vladimir Lotoreichik, Jonathan Rohleder

^*Corresponding author for this work

Institute of Applied Mathematics (5040)

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	895-916
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	147
Issue number	5
DOIs	https://doi.org/10.1017/S0308210516000421
Publication status	Published - 2017

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title = "Quasi boundary triples and semibounded self-adjoint extensions",

abstract = "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.",

author = "Jussi Behrndt and Matthias Langer and Vladimir Lotoreichik and Jonathan Rohleder",

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AU - Behrndt, Jussi

AU - Langer, Matthias

AU - Lotoreichik, Vladimir

AU - Rohleder, Jonathan

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

U2 - 10.1017/S0308210516000421

DO - 10.1017/S0308210516000421

M3 - Article

SN - 1473-7124

VL - 147

SP - 895

EP - 916

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

IS - 5

ER -

Quasi boundary triples and semibounded self-adjoint extensions

Abstract

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