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Journal of Spectral Theory


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Volume 9, Issue 2, 2019, pp. 379–427
DOI: 10.4171/JST/251

Published online: 2018-10-24

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

Laura Abatangelo[1], Veronica Felli[2], Luc Hillairet[3] and Corentin Léna[4]

(1) Università degli Studi di Milano-Bicocca, Italy
(2) Università degli Studi di Milano-Bicocca, Italy
(3) Université d’Orléans, France
(4) Stockholm University, Sweden

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.

Keywords: Asymptotics of eigenvalues, small capacity sets, Aharonov–Bohm operators

Abatangelo Laura, Felli Veronica, Hillairet Luc, Léna Corentin: Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators. J. Spectr. Theory 9 (2019), 379-427. doi: 10.4171/JST/251