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Fourier Transform of the Summatory Abel–Poisson Function

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Cybernetics and Systems Analysis Aims and scope

Abstract

The authors consider the current issues of the optimal decision theory, namely, the analysis of the asymptotic properties of the Fourier transform of the summatory Abel–Poisson function. The Fourier transform considered in the paper is based on the solution of the classical Laplace’s equation in polar coordinates (in the middle of the unit circle) with the corresponding boundary conditions. This Fourier transform of the summatory Abel–Poisson function is defined on the classes of fractional differential functions. The asymptotic estimates are obtained in the paper for this Fourier transform, which is an important element in solving many applied optimization problems.

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Authors and Affiliations

  1. Lesya Ukrainka Volyn National University, Lutsk, Ukraine

    T. V. Zhyhallo & Yu. I. Kharkevych

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  1. T. V. Zhyhallo
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Correspondence to T. V. Zhyhallo.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2022, pp. 120–129.

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Zhyhallo, T.V., Kharkevych, Y.I. Fourier Transform of the Summatory Abel–Poisson Function. Cybern Syst Anal 58, 957–965 (2022). https://doi.org/10.1007/s10559-023-00530-0

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