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A modified local Weyl law and spectral comparison results for $\delta'$-coupling conditions

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arxiv 2407.21719 v1 pith:MUW7AEKJ submitted 2024-07-31 math.SP math-phmath.MP

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keywords conditionscouplingdeltacomparisondistanceeigenvaluelimitinglocal
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abstract

We study Schr\"odinger operators on compact finite metric graphs subject to $\delta'$-coupling conditions. Based on a novel modified local Weyl law, we derive an explicit expression for the limiting mean eigenvalue distance of two different self-adjoint realisations on a given graph. Furthermore, using this spectral comparison result, we also study the limiting mean eigenvalue distance comparing $\delta'$-coupling conditions to so-called anti-Kirchhoff conditions, showing divergence and thereby confirming a numerical observation in [arXiv:2212.12531]. .

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Optimal geometric barriers for weighted observability of heat semigroups on metric measure spaces

    math.AP 2026-07 accept novelty 8.0 of 10

    If a heat-observability inequality with weight h holds from a set ω, then h(t) decays at least like exp(-κ L(ω)²/t) for every κ<1/2, yielding the sharp lower bound γ≥L(ω)²/2.

  2. Spectral comparison results for Laplacians on discrete graphs

    math.SP 2024-12 conditional novelty 4.0 of 10

    On discrete graphs with purely discrete spectrum, the summed eigenvalue difference between the Laplacian with and without a potential equals the weighted sum of the potential.

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