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

TitleOn spectral gaps of the Hill—Schrödinger operator with singular potential
Publication TypeJournal Article
Year of Publication2018
AuthorsMikhailets, VA, Molyboga, VM
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2018.10.003
Issue10
SectionMathematics
Pagination3-8
Date Published10/2018
LanguageRussian
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.
Keywordscontinuous spectrum, Hill's operator, spectral gap, strongly singular potential
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