Some inverse results for Hill's equation

Coskun H.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.276, no.2, pp.833-844, 2002 (SCI-Expanded) identifier identifier


We consider Hill's equation y" + (lambda - q)y = 0 where q is an element of L-1[0, pi]. We show that if l(n)-the length of the n-th instability interval-is of order O(n(-(k+2))) then the real Fourier coefficients a(n)(k), b(n)(k) of q((k))-k-th derivative of q-are of order O(n(-2)), which implies that q((k)) is absolutely continuous almost everywhere for k = 0, 1, 2..... (C) 2002 Elsevier Science (USA). All rights reserved.