Inverse problems associated with the Hill operator
Date
2016-01-27
Authors
Kirac, Alp Arslan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
Let 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.
Description
Keywords
Hill operator, Inverse spectral theory, Eigenvalue asymptotics, Fourier coefficients
Citation
Kiraç, A. A. (2016). Inverse problems associated with the Hill operator. Electronic Journal of Differential Equations, 2016(41), pp. 1-12.
Rights
Attribution 4.0 International