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  • 1. Abatangelo, Laura
    et al.
    Felli, Veronica
    Hillairet, Luc
    Léna, Corentin
    Stockholm University, Faculty of Science, Department of Mathematics.
    Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators2019In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 9, no 2, p. 379-427Article in journal (Refereed)
    Abstract [en]

    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.

  • 2. Behrndt, Jussi
    et al.
    Rohleder, Jonathan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Stadler, Simon
    Eigenvalue inequalities for Schrödinger operators on unbounded Lipschitz domains2018In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 8, no 2, p. 493-508Article in journal (Refereed)
    Abstract [en]

    Given a Schrödinger differential expression on an exterior Lipschitz domain we prove strict inequalities between the eigenvalues of the corresponding selfadjoint operators subject toDirichlet andNeumann orDirichlet andmixed boundary conditions, respectively. Moreover, we prove a strict inequality between the eigenvalues of two different elliptic differential operators on the same domain with Dirichlet boundary conditions.

  • 3.
    Kurasov, Pavel
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Naboko, Sergey
    Rayleigh estimates for differential operators on graphs2014In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 4, no 2, p. 211-219Article in journal (Refereed)
    Abstract [en]

    We study the spectral gap, i.e. the distance between the two lowest eigenvalues for Laplace operators on metric graphs. A universal lower estimate for the spectral gap is proven and it is shown that it is attained if the graph is formed by just one interval. Uniqueness of the minimizer allows to prove a geometric version of the Ambartsumian theorem derived originally for Schrodinger operators.

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