Kirac, Alp Arslan2023-06-122023-06-122016-01-27Kiraç, A. A. (2016). Inverse problems associated with the Hill operator. Electronic Journal of Differential Equations, 2016(41), pp. 1-12.1072-6691https://hdl.handle.net/10877/16915Let ℓn be the length of the n-th instability interval of the Hill operator Ly = -y″ + q(x)y. We prove that if ℓn = o(n-2) and the set {(nπ)2 : n is even and n > n0} is a subset of the periodic spectrum of the Hill operator, then q = 0 a.e., where n0 is a sufficiently large positive integer such that ℓn < εn-2 for all n > n0(ε) with some ε > 0. A similar result holds for the anti-periodic case.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalHill operatorInverse spectral theoryEigenvalue asymptoticsFourier coefficientsArticle