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 R 1−δ admits the estimate |ψ1(z)/ψ2(z) − 1| ≤ εR −μ(1−δ) if R ≥ R 0(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.
References
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Original Russian Text © V. L. Geynts, A. A. Shkalikov, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 6, pp. 887–896.
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Geynts, V.L., Shkalikov, A.A. Estimate of the ratio of two entire functions whose zeros coincide in the disk. Math Notes 99, 870–878 (2016). https://doi.org/10.1134/S0001434616050254
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DOI: https://doi.org/10.1134/S0001434616050254