Singularly perturbed periodic and semiperiodic differential operators

• Date: 2007
• Main Authors: Mikhailets, V. A., Molyboga, V. M., Михайлець, В. А., Молибога, В. М.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2007
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3345
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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-p...