Pré-Publication, Document De Travail Année : 2026

Dispersion for the Schrödinger equation on the line with short-range array of delta potentials

Résumé

We study dispersive properties of the one-dimensional Schrödinger equation with a short-range array of delta interactions. More precisely, we consider the self-adjoint operator obtained by perturbing the free Laplacian on the line with a real-valued sequence of Dirac delta potentials and belonging to weighted ℓ^1(Z) spaces. Under suitable decay assumptions on the coupling constants and in the absence of a zero-energy resonance, we establish the L^1 (R) → L^∞ (R) dispersive estimate with decay rate |t|^{-1/2} for the associated Schrödinger group. The proof relies on a limiting absorption principle in weighted spaces, explicit representation of the resolvent kernel in terms of Jost solutions and Born series expansion of the Friedrichs extension of the perturbed operator.

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Dates et versions

hal-05536796 , version 1 (04-03-2026)
hal-05536796 , version 2 (27-03-2026)

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Romain Duboscq, Élio Durand-Simonnet, Stefan Le Coz. Dispersion for the Schrödinger equation on the line with short-range array of delta potentials. 2026. ⟨hal-05536796v1⟩
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