Spectral estimates for resolvent differences of self-adjoint elliptic operators

Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The concept of quasi boundary triples and Weyl functions from extension theory of symmetric operators in Hilbert spaces is developed further and spectral estimates for resolvent differences of two self-adjoint extensions in terms of general operator ideals are proved. The abstract results are applied to self-adjoint realizations of second order elliptic differential operators on bounded and exterior domains, and partial differential operators with δ-potentials supported on hypersurfaces are studied.
LanguageEnglish
Pages1-37
Number of pages37
JournalIntegral Equations and Operator Theory
Volume77
Issue number1
Early online date1 Jul 2013
DOIs
Publication statusPublished - Sep 2013

Fingerprint

Weyl Function
Extension Theory
Operator Ideals
Self-adjoint Extension
Symmetric Operator
Partial Differential Operators
Exterior Domain
Self-adjoint Operator
Resolvent
Elliptic Operator
Hypersurface
Differential operator
Bounded Domain
Hilbert space
Estimate
Concepts

Keywords

  • elliptic operator
  • self-adjoint extension
  • operator ideal
  • delta-potential
  • quasi boundary triple
  • Weyl function

Cite this

@article{d198ab7af97141bd8f9f441675845f12,
title = "Spectral estimates for resolvent differences of self-adjoint elliptic operators",
abstract = "The concept of quasi boundary triples and Weyl functions from extension theory of symmetric operators in Hilbert spaces is developed further and spectral estimates for resolvent differences of two self-adjoint extensions in terms of general operator ideals are proved. The abstract results are applied to self-adjoint realizations of second order elliptic differential operators on bounded and exterior domains, and partial differential operators with δ-potentials supported on hypersurfaces are studied.",
keywords = "elliptic operator, self-adjoint extension, operator ideal, delta-potential, quasi boundary triple, Weyl function",
author = "Jussi Behrndt and Matthias Langer and Vladimir Lotoreichik",
note = "The final publication is available at Springer via http://dx.doi.org/10.1007{\%}2Fs00020-013-2072-2",
year = "2013",
month = "9",
doi = "10.1007/s00020-013-2072-2",
language = "English",
volume = "77",
pages = "1--37",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
number = "1",

}

Spectral estimates for resolvent differences of self-adjoint elliptic operators. / Behrndt, Jussi; Langer, Matthias; Lotoreichik, Vladimir.

In: Integral Equations and Operator Theory, Vol. 77, No. 1, 09.2013, p. 1-37.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Spectral estimates for resolvent differences of self-adjoint elliptic operators

AU - Behrndt, Jussi

AU - Langer, Matthias

AU - Lotoreichik, Vladimir

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007%2Fs00020-013-2072-2

PY - 2013/9

Y1 - 2013/9

N2 - The concept of quasi boundary triples and Weyl functions from extension theory of symmetric operators in Hilbert spaces is developed further and spectral estimates for resolvent differences of two self-adjoint extensions in terms of general operator ideals are proved. The abstract results are applied to self-adjoint realizations of second order elliptic differential operators on bounded and exterior domains, and partial differential operators with δ-potentials supported on hypersurfaces are studied.

AB - The concept of quasi boundary triples and Weyl functions from extension theory of symmetric operators in Hilbert spaces is developed further and spectral estimates for resolvent differences of two self-adjoint extensions in terms of general operator ideals are proved. The abstract results are applied to self-adjoint realizations of second order elliptic differential operators on bounded and exterior domains, and partial differential operators with δ-potentials supported on hypersurfaces are studied.

KW - elliptic operator

KW - self-adjoint extension

KW - operator ideal

KW - delta-potential

KW - quasi boundary triple

KW - Weyl function

UR - http://link.springer.com/journal/volumesAndIssues/20

U2 - 10.1007/s00020-013-2072-2

DO - 10.1007/s00020-013-2072-2

M3 - Article

VL - 77

SP - 1

EP - 37

JO - Integral Equations and Operator Theory

T2 - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -