C&SA | Contents

Volume 57 >>> № 6 NOVEMBER — DECEMBER 2021

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UDC 517.95

I.M. Alexandrovich¹, S.I. Lyashko², M.V-S. Sydorov³,
N.I. Lyashko⁴, O.S. Bondar⁵

¹ Taras Shevchenko National University of Kyiv,
Kyiv, Ukraine

ialexandrovich@ukr.net

² Taras Shevchenko National University of Kyiv,
Kyiv, Ukraine

lyashko.serg@gmail.com

³ Taras Shevchenko National University of Kyiv,
Kyiv, Ukraine

myksyd@knu.ua

⁴ V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

lyashko.natali@gmail.com

⁵ Taras Shevchenko National University of Kyiv,
Kyiv, Ukraine

alenkajob@gmail.com

RIEMANN INTEGRAL OPERATOR FOR STATIONARY AND NON-STATIONARY PROCESSES

Abstract. Integral operators based on the Riemann function, which transform arbitrary analytical functions into regular solutions of equations of elliptic, parabolic, and hyperbolic types of second order are constructed. The Riemann operator method is generalized for the biaxisymmetric Helmholtz equation. A method for finding solutions of the above equations in analytical form is developed. In some cases, formulas for inverting integral representations of solutions are constructed. The conditions for solving the Cauchy problem for the axisymmetric Helmholtz equation are formulated.

Keywords: integral operator, regular solutions, analytical functions.

FULL TEXT

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