Spectral estimates for resolvent differences of self-adjoint elliptic operators

Jussi Behrndt; Matthias Langer; Vladimir Lotoreichik

doi:10.1007/s00020-013-2072-2

Spectral estimates for resolvent differences of self-adjoint elliptic operators

Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik

Mathematics And Statistics

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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.

Original language	English
Pages (from-to)	1-37
Number of pages	37
Journal	Integral Equations and Operator Theory
Volume	77
Issue number	1
Early online date	1 Jul 2013
DOIs	https://doi.org/10.1007/s00020-013-2072-2
Publication status	Published - Sept 2013

Keywords

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

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10.1007/s00020-013-2072-2

behrndt-etal-IEOT2013-resolvent-differences-of-self-adjoint-elliptic-operatorsAccepted author manuscript, 354 KB

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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.",

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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

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DO - 10.1007/s00020-013-2072-2

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SP - 1

EP - 37

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 1

ER -

Spectral estimates for resolvent differences of self-adjoint elliptic operators

Abstract

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Spectral Theory of Block Operator Matrices

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Spectral estimates for resolvent differences of self-adjoint elliptic operators

Abstract

Keywords

Access to Document

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Fingerprint

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Spectral Theory of Block Operator Matrices

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