Smoothness of Hill’s Potential and Lengths of Spectral Gaps

  • Vladimir MikhailetsEmail author
  • Volodymyr Molyboga
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 221)


The paper studies the Hill–Schrödinger operators with potentials in the space \({H^\omega}\subset{L^2}(\mathbb{T},\mathbb{R}).\) Explicit description for the classes of sequences being the lengths of spectral gaps of these operators is found. The functions ω may be nonmonotonic. The space \({H^\omega}\) coincides with the Hörmander space \({H^\omega_2}(\mathbb{T},\mathbb{R}), \) with the weight function \(\omega(\sqrt{1+\xi^2})\) if ω is in Avakumovich’s class OR.


Hill–Schrödinger operators spectral gaps Hörmander spaces. 


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© Springer Basel 2012

Authors and Affiliations

  1. 1.Institute of MathematicsNational Academy of Science of UkraineKyiv-4Ukraine

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