Dergiler / Turkish Journal of Mathematics / 2000 / Cilt: 24 - Sayı: 1
On the Asymptotics of Fourier Coefficients for the Potential in Hill's Equation
- Sayfa
- 15–24
- DOI
- —
Özet
We consider Hill's equation y'' +(l -q)y=0 where q\in L1[0,p ]. We show that if ln-the length of the n-th instability interval- is of order O(n-k) then the real Fourier coefficients an,bn of q are of the same order for(k=1,2,3), which in turn implies that q(k-2), the (k-2)th derivative of q, is absolutely continuous almost everywhere for k=2,3.
Abstract
We consider Hill's equation y'' +(l -q)y=0 where q\in L1[0,p ]. We show that if ln-the length of the n-th instability interval- is of order O(n-k) then the real Fourier coefficients an,bn of q are of the same order for(k=1,2,3), which in turn implies that q(k-2), the (k-2)th derivative of q, is absolutely continuous almost everywhere for k=2,3.