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UDC 519.8
T.V. Zhyhallo1, Yu.I. Kharkevych2


1 Lesya Ukrainka Volyn National University, Lutsk, Ukraine

 tetvas@ukr.net

2 Lesya Ukrainka Volyn National University, Lutsk, Ukraine

 kharkevich.juriy@gmail.com

FOURIER TRANSFORM OF THE SUMMING ABEL–POISSON FUNCTION

Abstract. The work is devoted to the current issues of the theory of optimal solutions, namely the analysis of the asymptotic properties of the Fourier transformation of the summing 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 single circle) with the corresponding boundary conditions. Moreover, this Fourier transform of the summing Abel–Poisson function is denoted by classes of functions with fractional derivatives. Therefore, the asymptotic estimates obtained in the paper for this Fourier transform are an important element in solving many applied optimization problems.

Keywords: theory of optimal solutions, optimization problems, Fourier transform, asymptotic properties.


FULL TEXT

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