1-D Schrödinger operators with distributional potentials.

1. V. Mikhailets, V. Molyboga, “One-dimensional Schrödinger operators with singular periodic potentials”, The one-dimensional Schrödinger operators $S(q)u:=-u''+q(x)u$, $u\in\mathrm{Dom}(S(q))$ with 1-periodic real-valued singular potentials $q(x)\in H_{per}^{-1}(\mathbb{R},\mathbb{R})$ are studied on the Hilbert space $L_2(\mathbb{R})$. An equivalence of five basic definitions for the operators $S(q)$ and their self-adjointness are established. A new proof of spectral continuity of the operators $S(q)$ is found. Endpoints of spectral gaps are precisely described, Methods Funct. Anal. Topology, 14:2 (2008), 184–200
2. V. Mikhailets, V. Molyboga, “Singularly perturbed periodic and semiperiodic differential operators”, Ukrainian Math. J., 59:6 (2007), 785–797      

• Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev