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Resonance distributions for 1D Schrödinger operators

Published on:

1 November 2023

Primary Category:

Mathematical Physics

Paper Authors:

T. J. Christiansen,

T. Cunningham

Bullets

Key Details

Proves upper bound on resonance density above logarithmic curves in terms of singular support

Explicitly constructs potentials producing multiple resonance sequences along distinct logarithmic curves

Shows resonances in sectors away from real axis are stable under perturbations

Uses integral representation of scattering matrix to relate singularities and resonance asymptotics

Applies Hardy's method and Rouché's theorem to locate resonance sequences

AI generated summary

Resonance distributions for 1D Schrödinger operators

This paper studies the relationship between singularities in a potential and the asymptotic distribution of resonances for the associated 1D Schrödinger operator. Key results provide upper bounds on resonance density in terms of singular support, construct potentials producing multiple resonance sequences along distinct logarithmic curves, and prove stability of resonances in sectors away from the real axis.

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