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. <i>Electronic Journal of Differential Equations, 2016</i>(41), pp. 1-12.

Rights

Attribution 4.0 International

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