Open Access

Hill's potentials in Hörmander spaces and their spectral gaps


Abstract

The paper deals with the Hill-Schrödinger operators with singular periodic potentials in the space $H^{\omega}(\mathbb{T})\subset H^{-1}(\mathbb{T})$. The authors exactly describe the classes of sequences being the lengths of spectral gaps of these operators. The functions $\omega$ may be nonmonotonic. The space $H^{\omega}(\mathbb{T})$ coincides with the Hörmander space $H_{2}^{\omega}(\mathbb{T})$ with the weight function $\omega(\sqrt{1+\xi^{2}})$ if $\omega$ is in the Avakumovich class $\mathrm{OR}$.


Full Text





Article Information

TitleHill's potentials in Hörmander spaces and their spectral gaps
SourceMethods Funct. Anal. Topology, Vol. 17 (2011), no. 3, 235-243
MathSciNet MR2857727
CopyrightThe Author(s) 2011 (CC BY-SA)

Authors Information

V. A. Mikhailets
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

V. M. Molyboga
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 


Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley



Citation Example

V. A. Mikhailets and V. M. Molyboga, Hill's potentials in Hörmander spaces and their spectral gaps, Methods Funct. Anal. Topology 17 (2011), no. 3, 235-243.


BibTex

@article {MFAT589,
    AUTHOR = {Mikhailets, V. A. and Molyboga, V. M.},
     TITLE = {Hill's potentials in Hörmander spaces and their spectral gaps},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {17},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {235-243},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=589},
}


All Issues