Abstract
The paper is concerned with the spectral properties of the Schrödinger operator Lq def= − d2/dx2 + q with periodic potential q from the Sobolev space H −1 (T1 ). We obtain asymptotic formulas and a priori estimates for the periodic and Dirichlet eigenvalues which generalize known results for the case of potentials q ∈ L 2 0 (T1 ). The key idea is to reduce the problem to a known one – the spectrum of the impedance operator – via a nonlinear analytic isomorphism of the Sobolev spaces H −1 0 (T1 ) and L2 0 (T1 ).
Kappeler, T