Weak coupling and spectral instability for Neumann Laplacians

Jussi Behrndt; Fritz Gesztesy; Henk de Snoo

doi:10.1090/proc/17115

Weak coupling and spectral instability for Neumann Laplacians

Jussi Behrndt, Fritz Gesztesy, Henk de Snoo

Bernoulli Institute

Onderzoeksoutput: Article › Academic › peer review

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We prove an abstract criterion on spectral instability of nonnegative selfadjoint extensions of a symmetric operator and apply this to selfadjoint Neumann Laplacians on bounded Lipschitz domains, intervals, and graphs. Our results can be viewed as variants of the classical weak coupling phenomenon for Schrödinger operators in L²(Rⁿ) for n = 1, 2.

Originele taal-2	English
Pagina's (van-tot)	1675-1686
Aantal pagina's	12
Tijdschrift	Proceedings of the american mathematical society
Volume	153
Nummer van het tijdschrift	4
DOI's	https://doi.org/10.1090/proc/17115
Status	Published - apr.-2025

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Weak coupling and spectral instability for Neumann Laplacians
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title = "Weak coupling and spectral instability for Neumann Laplacians",

abstract = "We prove an abstract criterion on spectral instability of nonnegative selfadjoint extensions of a symmetric operator and apply this to selfadjoint Neumann Laplacians on bounded Lipschitz domains, intervals, and graphs. Our results can be viewed as variants of the classical weak coupling phenomenon for Schr{\"o}dinger operators in L2(Rn) for n = 1, 2.",

keywords = "Birman–Schwinger principle, Neumann Laplacian, Schr{\"o}dinger operator, spectral instability, Weakly coupled bound state",

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AU - Gesztesy, Fritz

AU - de Snoo, Henk

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N2 - We prove an abstract criterion on spectral instability of nonnegative selfadjoint extensions of a symmetric operator and apply this to selfadjoint Neumann Laplacians on bounded Lipschitz domains, intervals, and graphs. Our results can be viewed as variants of the classical weak coupling phenomenon for Schrödinger operators in L2(Rn) for n = 1, 2.

AB - We prove an abstract criterion on spectral instability of nonnegative selfadjoint extensions of a symmetric operator and apply this to selfadjoint Neumann Laplacians on bounded Lipschitz domains, intervals, and graphs. Our results can be viewed as variants of the classical weak coupling phenomenon for Schrödinger operators in L2(Rn) for n = 1, 2.

KW - Birman–Schwinger principle

KW - Neumann Laplacian

KW - Schrödinger operator

KW - spectral instability

KW - Weakly coupled bound state

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JO - Proceedings of the american mathematical society

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Weak coupling and spectral instability for Neumann Laplacians

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