One-dimensional Schrödinger operators with singular periodic potentials - Molyboga, V. M.; Mikhailets, V. A. (Methods of Functional Analysis and Topology, 2008)
We study the one-dimensional Schrödinger operators S(q)u:=-u’’+q(x)u,uDom(S(q) ), with 1-periodic real-valued singular potentials q(x)H_per ^-1(R,R) on the Hilbert space L_2(R ). We show equivalence of five basic definitions of the operators S(q) and prove that they are self-adjoint. A new proof of continuity of the spectrum of the operators S(q) is found. Endpoints of spectrum gaps are precisely described.