V. L. Geynts, A. Shkalikov

Jun 29, 2016

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Mathematical Notes

Abstract

We study entire functions of finite growth order that admit the representation ψ(z) = 1 + O(|z|−μ), μ > 0, on a ray in the complex plane. We obtain the following result: if the zeros of two functions ψ1, ψ2 of such class coincide in the disk of radius R centered at zero, then, for any arbitrarily small δ ∈ (0, 1), ε > 0, the ratio of these functions in the disk of radius R1−δ admits the estimate |ψ1(z)/ψ2(z) − 1| ≤ εR−μ(1−δ) if R ≥ R0(ε, δ). The obtained results are important for stability analysis in the problem of the recovery of the potential in the Schrödinger equation on the semiaxis from the resonances of the operator.

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