Spectral gaps of one-dimensional Schrödinger operators with singular periodic potentials
The behavior of the lengths of spectral gaps {γ_n(q)}_n=1^∞ of the Hill-Schrödinger operators S(q)u=-u’’+q(x)u,uDom(S(q) ), with real-valued 1-periodic distributional potentials q(x)H_1-per ^-1(R) is studied. We show that they exhibit the same behavior as the Fourier coefficients {q(n)}_n=-∞^∞ of the potentials q(x) with respect to the weighted sequence spaces h^s,φ, s>-1, φSV. The case q(x)L_1-per ^2(R), sZ_+, φ1, corresponds to the Marchenko-Ostrovskii Theorem., number=1, journal=Methods of Functional Analysis and Topology, author=Molyboga, V. M. and Mikhailets, V. A., year=2009, month=Mar., pages=31–40