SPECTRAL GAPS OF THE ONE-DIMENSIONAL SCHRODINGER OPERATORS WITH SINGULAR PERIODIC POTENTIALS

The behavior of the lengths of spectral gaps {gamma(n)(q)}(n=1)infinity of the Hill-Schrodinger operators S(q)u =-u '' + q(x)u, u is an element of Dom (S(q)), with real-valued 1-periodic distributional potentials q(x) is an element of H-1-per(-1) (R) is studied. We show that they exhibit the same behavior as the Fourier coefficients {(q) over cap (n)}(n=-infinity)(infinity) of the potentials q(x) with respect to the weighted sequence spaces h(delta,phi) s >-1, phi is an element of SV. The case q(x) is an element of L-1-per(2)(R), s is an element of z(+), phi equivalent to 1, corresponds to the Marchenko-Ostrovskii Theorem.