Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation with Smooth Potential

Authors

  • O. M. Denysenko
  • I. O. Parasyuk

Abstract

A one-dimensional Schrödinger equation with a potential characterized by a certain rate of approximation by trigonometric polynomials is investigated by methods of the KAM theory. Estimates for resonance energy zones are obtained. The case where the potential belongs to the Gevrey class is analyzed.

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Published

25.01.2004

Issue

Vol. 56 No. 1 (2004)

Section

Research articles

How to Cite

Denysenko, O. M., and I. O. Parasyuk. “Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation With Smooth Potential”. Ukrains’kyi Matematychnyi Zhurnal, vol. 56, no. 1, Jan. 2004, pp. 3-18, https://umj.imath.kiev.ua/index.php/umj/article/view/3724.