Some inverse results for Hill's equation
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.276, no.2, pp.833-844, 2002 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 276 Issue: 2
- Publication Date: 2002
- Doi Number: 10.1016/s0022-247x(02)00454-7
- Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.833-844
- Keywords: Hill's equation, Fourier coefficients, asymptotics, EIGENVALUES
- Karadeniz Technical University Affiliated: Yes
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.