УДК 519.8

Д.В. ШАПОВАЛОВ
Волинський національний університет імені Лесі Українки, Луцьк, Україна,
 shapovalovdv@ukr.net

А.М. ШУТОВСЬКИЙ
Волинський національний університет імені Лесі Українки, Луцьк, Україна,
 sh93ar@gmail.com

АСИМПТОТИЧНІ ВЛАСТИВОСТІ ДЕЯКОЇ СИСТЕМИ
ОРТОГОНАЛЬНИХ МНОГОЧЛЕНІВ

СПИСОК ЛІТЕРАТУРИ

• 1. Advanced Control Systems: Theory and Applications. Edited by Yuriy P. Kondratenko, Vsevolod M. Kuntsevich, Arkadii A. Chikrii, Vyacheslav F. Gubarev, 1st Edition. New York: River Publishers, 2021. 476 p. https://doi.org/10.1201/9781003337010.
• 2. Kharkevych Yu. Approximation theory and related applications. Axioms. 2022. Vol. 11, N 12, 736. https://doi.org/10.3390/axioms11120736.
• 3. Vlasenko L.A., Chikrii A.A. On a differential game in a system with distributed parameters. Proceedings of the Steklov Institute of Mathematics. 2016. Vol. 292, Suppl 1. P. 276–285. https://doi.org/10.1134/S0081543816020243.
• 4. Korenkov M., Kharkevych Yu. On the asymptotics and distribution of values of the Jacobi theta functions and the estimate of the type of the Weierstrass sigma functions. Axioms. 2022. Vol. 11, N 1, 12. https://doi.org/10.3390/axioms11010012.
• 5. Chikrii A.A., Belousov A.A. On linear differential games with integral constraints. Proceedings of the Steklov Institute of Mathematics. 2010. Vol. 269, Suppl 1. P. 69–80. https://doi.org/10.1134/S0081543810060076.
• 6. Abdullayev F.G., Bushev D.M., Imashkyzy M., Kharkevych Yu.I. Isometry of the subspaces of solutions of systems of differential equations to the spaces of real functions. Ukrainian Mathematical Journal. 2020. Vol. 71, N 8. P. 1153–1172. https://doi.org/10.1007/s11253-019-01705-9.
• 7. Chikrii A.A., Matychyn I.I., Chikrii K.A. Differential games with impulse control. Annals of the International Society of Dynamic Games. 2007. Vol. 9. P. 37–55. https://doi.org/10.1007/978-0-8176-4553-3_2.
• 8. Nakonechnyi A.G., Kapustian E.A., Chikrii A.A. Control of impulse systems in conflict situation. Journal of Automation and Information Sciences. 2019. Vol. 51, N 9. P. 1–11. https://doi.org/10.1615/JAutomatInfScien.v51.i9.10.
• 9. Shutovskyi A.M. On approximation of functions from Hlder classes by biharmonic Poisson integrals defined in the upper half-plane. Journal of Mathematical Sciences. 2024. Vol. 282, N 1. P. 74–82. https://doi.org/10.1007/s10958-024-07169-y.
• 10. Zhyhallo K.M., Kharkevych Yu.I. On some approximate properties of biharmonic Poisson integrals in the integral metric. Carpathian Mathematical Publications. 2024. Vol. 16, N 1. P. 303–308. https://doi.org/10.15330/cmp.16.1.303-308.
• 11. Shutovskyi A.M., Pryt V.V. On the estimate of the biharmonic Poisson integral deviation from its boundary values in terms of the modulus of continuity. Journal of Mathematical Sciences. 2024. Vol. 285, N 5. P. 732–742. https://doi.org/10.1007/s10958-024-07471-9.
• 12. Kharkevych Yu.I., Shutovskyi A.M. Approximation of functions from Hlder class by biharmonic Poisson integrals. Carpathian Mathematical Publications. 2024. Vol. 16, N 2. P. 631–637. https://doi.org/10.15330/cmp.16.2.631-637.
• 13. Shutovskyi A.M., Zhyhallo K.M. On polyharmonic Poisson–Taylor operators. Journal of Mathematical Sciences. 2025. Vol. 288, N 5. P. 639–650. https://doi.org/10.1007/s10958-025-07748-7.
• 14. Zhyhallo T.V., Kharkevych Yu.I. Some asymptotic properties of the solutions of Laplace equations in a unit disk. Cybernetics and Systems Analysis. 2023. Vol. 59, N 3. P. 449–456. https://doi.org/10.1007/s10559-023-00579-x.
• 15. Bushev D.N., Kharkevich Yu.I. Finding solution subspaces of the Laplace and heat equations isometric to spaces of real functions, and some of their applications. Mathematical Notes. 2018. Vol. 103, N 5–6. P. 869–880. https://doi.org/10.1134/S0001434618050231.
• 16. Zhigallo K.M., Kharkevych Yu.I. On the approximation of functions of the Hlder class by biharmonic Poisson integrals. Ukrainian Mathematical Journal. 2000. Vol. 52, N 7. P. 1113–1117. https://doi.org/10.1023/A:1005285818550.
• 17. Kharkevych Yu.I., Zhyhallo T.V. Approximation of (ψ, β )-differentiable functions defined on the real axis by Abel–Poisson operators. Ukrainian Mathematical Journal. 2005. Vol. 57, N 8. P. 1297–1315. https://doi.org/10.1007/s11253-005-0262-z.
• 18. Zhyhallo T.V., Kharkevych Yu.I. Fourier transform of the summatory Abel–Poisson function. Cybernetics and Systems Analysis. 2022. Vol. 58, N 6. P. 957–965. https://doi.org/10.1007/s10559-023-00530-0.
• 19. Kharkevych Yu.I., Stepaniuk T.A. Approximate properties of Abel–Poisson integrals on classes of differentiable functions defined by moduli of continuity. Carpathian Mathematical Publications. 2023. Vol. 15, N 1. P. 286–294. https://doi.org/10.15330/cmp.15.1.286-294.
• 20. Shutovskyi A.M., Kharkevych Yu.I. On saturation of one linear method for summing Fourier series given by a function set. Researches in Mathematics. 2025. Vol. 33, N 1. P. 122–136. https://doi.org/10.15421/242508.
• 21. Bushev D.M., Kharkevych Yu.I. Approximation of classes of periodic multivariable functions by linear positive operators. Ukrainian Mathematical Journal. 2006. Vol. 58, N 1. P. 12–21. https://doi.org/10.1007/s11253-006-0048-y.
• 22. Shutovskyi A.M. Integral representations of polyharmonic operators. Cybernetics and Systems Analysis. 2025. Vol. 61, N 3. P. 450–460. https://doi.org/10.1007/s10559-025-00782-y.
• 23. Kharkevych Yu.I. Exact values of the approximations of differentiable functions by Poisson-type integrals. Cybernetics and Systems Analysis. 2023. Vol. 59, N 2. P. 274–282. https://doi.org/10.1007/s10559-023-00561-7.
• 24. Kal’chuk I., Kharkevych Yu. Approximation properties of the generalized Abel–Poisson integrals on the Weyl–Nagy classes. Axioms. 2022. Vol. 11, N 4, 161. https://doi.org/10.3390/axioms11040161.
• 25. Kharkevych Yu.I. Asymptotic expansions of upper bounds of deviations of functions of class W ^r from their generalized Poisson integrals. Journal of Automation and Information Sciences. 2018. Vol. 50, N 8. P. 38–49. https://doi.org/10.1615/JAutomatInfScien.v50.i8.40.
• 26. Baranovskaya L.V., Chikrii A.A., Chikrii Al.A. Inverse Minkowski functional in a nonstationary problem of group pursuit. Journal of Computer and Systems Sciences International. 1997. Vol. 36, N 1. P. 101–106.
• 27. Zając J., Korenkov M.E., Kharkevych Yu.I. On the asymptotics of some Weierstrass functions. Ukrainian Mathematical Journal. 2015. Vol. 67, N 1. P. 154–158. https://doi.org/10.1007/s11253-015-1070-8.
• 28. Vlasenko L.A., Rutkas A.G., Semenets V.V., Chikrii A.A. On the optimal impulse control in descriptor systems. Journal of Automation and Information Sciences. 2019. Vol. 51, N 5. P. 1–15. https://doi.org/10.1615/JAutomatInfScien.v51.i5.10.
• 29. Kharkevych Yu.I., Khanin O.G. Asymptotic properties of the solutions of higher-order differential equations on generalized Holder classes. Cybernetics and Systems Analysis. 2023. Vol. 59, N 4. P. 633–639. https://doi.org/10.1007/s10559-023-00598-8.