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 $\mathrm{OR}$.
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Article Information
Title
Hill's potentials in Hörmander spaces and their spectral gaps
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},
}