Zhyhallo T.V., Kharkevych Y.I.
Fourier transform of the summing Abel–Poisson function

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. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: asymptotic properties, Fourier transform, optimal decision theory, optimization problem, Fourier transforms, Optimization, 'current, Asymptotic properties, Differential functions, Fractional differential, Optimal decision theory, Optimal decisions, Optimization problems, Poisson functions, Polar coordinate, Unit circles, Decision theory

Cite:
Zhyhallo T.V., Kharkevych Y.I. (2022). Fourier transform of the summing Abel–Poisson function. Cybernetics and Systems Analysis, 58 (6), 120–129. doi: https://doi.org/10.1007/s10559-023-00530-0 http://jnas.nbuv.gov.ua/article/UJRN-0001368556 [In Ukrainian].