2017
Том 69
№ 7

All Issues

Singularly perturbed periodic and semiperiodic differential operators

Mikhailets V. A., Molyboga V. M.

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Abstract

Qualitative and spectral properties of the form sums $$S_{±}(V) := D^{2m}_{±} + V(x),\quad m ∈ N,$$ are studied in the Hilbert space $L_2(0, 1)$. Here, $(D_{+})$ is a periodic differential operator, $(D_{-})$ is a semiperiodic differential operator, $D_{±}: u ↦ −iu′$, and $V(x)$ is an arbitrary 1-periodic complex-valued distribution from the Sobolev spaces $H_{per}^{−mα},\; α ∈ [0, 1]$.

English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 6, pp 858-873.

Citation Example: Mikhailets V. A., Molyboga V. M. Singularly perturbed periodic and semiperiodic differential operators // Ukr. Mat. Zh. - 2007. - 59, № 6. - pp. 785–797.

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