Some inverse results for Hill's equation


Coskun H.

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

  • Publication Type: Article / Article
  • Volume: 276 Issue: 2
  • Publication Date: 2002
  • Doi Number: 10.1016/s0022-247x(02)00454-7
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.833-844

Abstract

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.