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

 Title On spectral gaps of the Hill—Schrödinger operator with singular potential Publication Type Journal Article Year of Publication 2018 Authors Mikhailets, VA, Molyboga, VM Abbreviated Key Title Dopov. Nac. akad. nauk Ukr. DOI 10.15407/dopovidi2018.10.003 Issue 10 Section Mathematics Pagination 3-8 Date Published 10/2018 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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