УДК 519.8

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

ДЕЯКІ ПРЕДСТАВЛЕННЯ ТРИГАРМОНІЙНИХ ФУНКЦІЙ

СПИСОК ЛІТЕРАТУРИ

• 1. Chikrii A.A., Petryshyn R., Cherevko I., Bigun Y. Method of resolving functions in the theory of conflict–controlled processes. Studies in Systems, Decision and Control. 2019. Vol. 203. P. 3–33. URL: https://doi.org/10.1007/978-3-030-21927-7_1 .


• 2. Chikrij A.A., Dzyubenko K.G. Bilinear markovian processes of search for moving objects. Problemy Upravleniya i Informatiki (Avtomatika). 1997. Iss. 1. P. 92–106


• 3. Prokopovich P.V., Chikrii A.A. A linear evasion problem for interacting groups of objects. Journal of Applied Mathematics and Mechanics. 1994. Vol. 58, N 4. P. 583–591. URL: https://doi.org/10.1016/0021-8928(94)90135-X .


• 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, Iss. 1. P. 12–22. URL: https://doi.org/10.3390/axioms11010012 .


• 5. 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, Iss. 1. P. 286–294. URL: https://doi.org/10.15330 .


• 6. Zhyhallo K.M., Kharkevych Yu.I. On some approximate properties of biharmonic Poisson integrals in the integral metric. Carpathian Mathematical Publications. 2024. Vol. 16, Iss. 1. P. 303–308. URL: https://doi.org/10.15330 .


• 7. 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. URL: https://doi.org/10.1615 .


• 8. Kharkevych Yu. Approximation theory and related applications. Axioms. 2022. Vol. 11, Iss. 12. P. 736. URL: https://doi.org/10.3390 .


• 9. 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. URL: https://doi.org/10.1134 .


• 10. Korenkov M.E., Kharkevych Yu.I. On the asymptotics of associated sigma-functions and Jacobi theta-functions. Ukrainian Mathematical Journal. 2019. Vol. 70, N 8. P. 1326–1330. URL: https://doi.org/10.1007 .


• 11. 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. URL: https://doi.org/10.1007 .


• 12. 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. URL: https://doi.org/10.1007 .


• 13. 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. URL: https://doi.org/10.1134 .


• 14. 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. URL: https://doi.org/10.1134 .


• 15. Kharkevych Yu.I. On some asymptotic properties of solutions to biharmonic equations. Cybernetics and Systems Analysis. 2022. Vol. 58, N 2. P. 251–258. URL: https://doi.org/10.1007 .


• 16. Zhyhallo K.M., Kharkevych Yu.I. Approximation of conjugate differentiable functions by their Abel–Poisson integrals. Ukrainian Mathematical Journal. 2009. Vol. 61, N 1. P. 86–98. URL: https://doi.org/10.1007 .


• 17. Kharkevych Yu.I., Khanin O.G. Asymptotic properties of the solutions of higher-order differential equations on generalized Hölder classes. Cybernetics and Systems Analysis. 2023. Vol. 59, N 4. P. 633–639. URL: https://doi.org/10.1007 .


• 18. Zhyhallo K.M., Kharkevych Yu.I. Approximation of conjugate differentiable functions by biharmonic Poisson integrals. Ukrainian Mathematical Journal. 2009. Vol. 61, N 3. P. 399–413. URL: https://doi.org/10.1007 .


• 19. Shutovskyi A.M., Sakhnyuk V.Ye. Representation of Weierstrass integral via Poisson integrals. Journal of Mathematical Sciences (United States). 2021. Vol. 259, N 1. P. 97–103. URL: https://doi.org/10.1007 .


• 20. Zhyhallo K.M., Kharkevych Yu.I. Complete asymptotics of the deviation of a class of differentiable functions from the set of their harmonic Poisson integrals. Ukrainian Mathematical Journal. 2002. Vol. 54, N 1. P. 51–63. URL: https://doi.org/10.1023 .


• 21. Zhyhallo K.M., Kharkevych Yu.I. Approximation of differentiable periodic functions by their biharmonic Poisson integrals. Ukrainian Mathematical Journal. 2002. Vol. 54, N 9. P. 1462–1470. URL: https://doi.org/10.1023 .


• 22. Hrabova U.Z., Kal’chuk I.V. Approximation of classes C 
  ^ψ _β,∞
  by three-harmonic Poisson integrals in uniform metric (Low Smoothness). Journal of Mathematical Sciences (United States). 2022. Vol. 268, N 2. P. 178–191. https://doi.org/10.1007/s10958-022-06190-3"target=_blank> https://doi.org/10.1007 .


• 23. 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. URL: https://doi.org/10.1007 .


• 24. Shutovskyi A.M. Some applied aspects of the Dirac delta function. Journal of Mathematical Sciences (United States). 2023. Vol. 276, N 5. P. 685–694. URL: https://doi.org/10.1007 .


• 25. Kal’chuk I.V., Kharkevych Yu.I. Approximation of the classes W 
  ^R _β,∞
  by generalized Abel–Poisson integrals. Ukrainian Mathematical Journal. 2022. Vol. 74, N 4. P. 575–585. URL: https://doi.org/10.1007 .


• 26. Zhyhallo T.V., Kharkevych Yu.I. On approximation of functions from the class L 
  ^ψ _β,1
  by the Abel–Poisson integrals in the integral metric. Carpathian Mathematical Publications. 2022. Vol. 14, Iss. 1. P. 223–229. URL: https://doi.org/10.15330 .


• 27. 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. URL: https://doi.org/10.1007 .


• 28. Kal’chuk I.V., Kharkevych Yu.I. Approximating properties of biharmonic Poisson integrals in the classes W 
  ^ψ _r,β
   H ^α. Ukrainian Mathematical Journal. 2017. Vol. 68, N 11. P. 1727–1740. URL: https://doi.org/10.1007 .


• 29. Zhyhallo K.M., Kharkevych Yu.I. Approximation of functions from the classes C 
  ^ψ _β,∞
  by biharmonic Poisson integrals. Ukrainian Mathematical Journal. 2011. Vol. 63, N 7. P. 1083–1107. URL: https://doi.org/10.1007 .


• 30. Shutovskyi A.M., Sakhnyuk V.Ye. Taylor series of biharmonic Poisson integral for upper half-plane. Journal of Mathematical Sciences (United States). 2022. Vol. 268, N 2. P. 239–246. URL: https://doi.org/10.1007 .


• 31. Hrabova U.Z., Kal’chuk I.V. Approximation of continuous functions given on the real axis by three-harmonic Poisson operators. Journal of Mathematical Sciences (United States). 2023. Vol. 274, N 3. P. 327–339. URL: https://doi.org/10.1007 .


• 32. 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. URL: https://doi.org/10.1007 .


• 33. Bushev D.M., Abdullayev F.G., Kal’chuk I.V., Imashkyzy M. The use of the isometry of function spaces with different numbers of variables in the theory of approximation of functions. Carpathian Mathematical Publications. 2021. Vol. 13, Iss. 3. P. 805–817. URL: https:// doi.org/10.15330 .


• 34. Shutovskyi A.M. On approximation of functions from Hölder classes by biharmonic Poisson integrals defined in the upper half-plane. Journal of Mathematical Sciences (United States). 2024. Vol. 282, N 1. P. 74–82. URL: https://doi.org/10.1007 .


• 35. Zhyhallo K.M., Kharkevych Yu.I. Approximation of (Ψ, β ) – differentiable functions of low smoothness by biharmonic Poisson integrals. Ukrainian Mathematical Journal. 2012. Vol. 63, N 12. P. 1820–1844. URL: https://doi.org/10.1007 .


• 36. 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. URL: https://doi.org/10.1007 .


• 37. Shutovskyi A.M. Some asymptotic properties of solutions to triharmonic equations. Cybernetics and Systems Analysis. 2024. Vol. 60, N 3. P. 472–479. URL: https://doi.org/10.1007 .


• 38. Zajc 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. URL: https://doi.org/10.1007 .


• 39. Pilipenko Yu.B., Chikrii A.A. Oscillatory conflict-control processes. Journal of Applied Mathematics and Mechanics. 1993. Vol. 57, N 3. P. 407–417. URL: https://doi.org/10.1016 .


• 40. 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, Iss. 1. P. 101–106


• 41. Chikrij A.A., Bezmagorychnyj V.V. Method of resolving functions in linear differential games with integral restrictions. Soviet Automatic Control. 1993. Iss. 4. P. 26–36


• 42. 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. URL: https://doi.org/10.1615 .


• 43. Chikrii A.A., Chikrii G.Ts. Game problems of approach for quasilinear systems of general form. Proceedings of the Steklov Institute of Mathematics. 2019. Vol. 304, Suppl 1. P. S44–S58. URL: https://doi.org/10.1134 .