On spectral gaps of the Hill—Schrödinger operator with singular potential
DOI:
https://doi.org/10.15407/dopovidi2018.10.003Keywords:
continuous spectrum, Hill's operator, spectral gap, strongly singular potentialAbstract
We study the continuous spectrum of the Hill—Schrödinger operator in a Hilbert space L2(R). The operator potential belongs to a Sobolev space Hloc−1(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 R is studied separately.
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