We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then we apply this spectral stability result to the study of the asymptotic behaviour of eigenvalues of Aharonov-Bohm operators with two colliding poles moving on an axis of symmetry of the domain.

Abatangelo, L., Felli, V., Hillairet, L., Lena, C. (2019). Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators. JOURNAL OF SPECTRAL THEORY, 9(2), 379-427 [10.4171/JST/251].

Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators

Abatangelo, L;Felli, V;
2019

Abstract

We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then we apply this spectral stability result to the study of the asymptotic behaviour of eigenvalues of Aharonov-Bohm operators with two colliding poles moving on an axis of symmetry of the domain.
Articolo in rivista - Articolo scientifico
Aharonov–Bohm operators; Asymptotics of eigenvalues; Small capacity sets
English
2019
9
2
379
427
partially_open
Abatangelo, L., Felli, V., Hillairet, L., Lena, C. (2019). Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators. JOURNAL OF SPECTRAL THEORY, 9(2), 379-427 [10.4171/JST/251].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/251814
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