Singularly perturbed periodic and semiperiodic differential operators

  • V. A. Mikhailets
  • V. M. Molyboga


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 $H_{per}^{−mα},\; α ∈ [0, 1]$.
How to Cite
MikhailetsV. A., and MolybogaV. M. “Singularly Perturbed Periodic and Semiperiodic Differential Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 6, June 2007, pp. 785–797,
Research articles