Spectral enclosures for non-self-adjoint extensions of symmetric operators

Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik, Jonathan Rohleder

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The spectral properties of non-self-adjoint extensions A[B] of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in terms of abstract boundary conditions involving an (in general non-symmetric) boundary operator B. In the abstract part of this paper, sufficient conditions for sectoriality and m-sectoriality as well as sufficient conditions for A[B] to have a non-empty resolvent set are provided in terms of the parameter B and the Weyl function. Special attention is paid to Weyl functions that decay along the negative real line or inside some sector in the complex plane, and spectral enclosures for A[B] are proved in this situation. The abstract results are applied to elliptic differential operators with local and non-local Robin boundary conditions on unbounded domains, to Schrödinger operators with δ-potentials of complex strengths supported on unbounded hypersurfaces or infinitely many points on the real line, and to quantum graphs with non-self-adjoint vertex couplings.
LanguageEnglish
Pages1808-1888
Number of pages81
JournalJournal of Functional Analysis
Volume275
Issue number7
DOIs
Publication statusPublished - 1 Oct 2018

Fingerprint

Weyl Function
Symmetric Operator
Enclosure
Real Line
Quantum Graphs
Robin Boundary Conditions
Nonlocal Boundary Conditions
Sufficient Conditions
Unbounded Domain
Resolvent
Elliptic Operator
Spectral Properties
Schrödinger Operator
Argand diagram
Hypersurface
Differential operator
Sector
Hilbert space
Decay
Boundary conditions

Keywords

  • non-self-adjoint extension
  • spectral enclosure
  • differential operator
  • Weyl function

Cite this

Behrndt, Jussi ; Langer, Matthias ; Lotoreichik, Vladimir ; Rohleder, Jonathan. / Spectral enclosures for non-self-adjoint extensions of symmetric operators. In: Journal of Functional Analysis. 2018 ; Vol. 275, No. 7. pp. 1808-1888.
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Spectral enclosures for non-self-adjoint extensions of symmetric operators. / Behrndt, Jussi; Langer, Matthias; Lotoreichik, Vladimir; Rohleder, Jonathan.

In: Journal of Functional Analysis, Vol. 275, No. 7, 01.10.2018, p. 1808-1888.

Research output: Contribution to journalArticle

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