Turkish Journal of Mathematics
DOI
-
Abstract
We consider Hill's equation $y'' +(\lambda -q)y=0$ where $q\in L^{1}[0,\pi ].$ We show that if $l_{n}-$the length of the $n-th$ instability interval$-$ is of order $O(n^{-k})$ then the real Fourier coefficients $a_{n},b_{n}$ 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 $k=2,3.$
First Page
15
Last Page
24
Recommended Citation
COŞKUN, HASKIZ (2000) "On the Asymptotics of Fourier Coefficients for the Potential in Hill's Equation," Turkish Journal of Mathematics: Vol. 24: No. 1, Article 2. Available at: https://journals.tubitak.gov.tr/math/vol24/iss1/2
