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# 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 $\mathrm{OR}$.

### Article Information

 Title Hill's potentials in Hörmander spaces and their spectral gaps Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 3, 235-243 MathSciNet MR2857727 Copyright The 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

### 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},
}