On spectral gaps of the Hill—Schrödinger operator with singular potential

1Mikhailets, VA, Molyboga, VM
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 10:3-8
https://doi.org/10.15407/dopovidi2018.10.003
Section: Mathematics
Language: Russian
Abstract: 
We study the continuous spectrum of the Hill—Schrödinger operator in a Hilbert space $L^{2}(\mathbb{R})$. The operator potential belongs to a Sobolev space ${H_{loc}}^{-1}(\mathbb{R})$. The conditions are found for the sequence of lengths of spectral gaps to: a) be bounded; b) converge to zero. The case where the potential is a real Radon measure on $\mathbb{R}$ is studied separately.
Keywords: continuous spectrum, Hill's operator, spectral gap, strongly singular potential
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