Singularly perturbed periodic and semiperiodic differential operators

Authors

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

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 $H_{per}^{−mα},\; α ∈ [0, 1]$.

Published

25.06.2007

Issue

Section

Research articles

How to Cite

Mikhailets, V. A., and V. M. Molyboga. “Singularly Perturbed Periodic and Semiperiodic Differential Operators”. Ukrains’kyi Matematychnyi Zhurnal, vol. 59, no. 6, June 2007, pp. 785–797, https://umj.imath.kiev.ua/index.php/umj/article/view/3345.