Some inverse results for Hill's equation
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.276, sa.2, ss.833-844, 2002 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 276 Sayı: 2
- Basım Tarihi: 2002
- Doi Numarası: 10.1016/s0022-247x(02)00454-7
- Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.833-844
- Anahtar Kelimeler: Hill's equation, Fourier coefficients, asymptotics, EIGENVALUES
- Karadeniz Teknik Üniversitesi Adresli: Evet
Özet
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.