Abstract
This 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 (T). We obtain asymptotic formulas and a priori estimates for the periodic and Dirichlet eigenvalues which generalize known results for the case of potentials q ∈ L2 (T). The key idea is to reduce the problem to a known one-the spectrum of the impedance operator-via a nonlinear analytic isomorphism between L02(T) and the Sobolev space H0-1(T). © 2004 Elsevier Inc. All rights reserved.
Kappeler, T