Singularly perturbed periodic and semiperiodic differential operators - Mikhailets, V. A.; Molyboga, V. M. (Ukrains’kyi Matematychnyi Zhurnal, 2007)
Qualitative and spectral properties of the form sums S_±(V) := D^2m_± + V(x),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].