УДК 519.8

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

ІНТЕГРАЛЬНІ ПРЕДСТАВЛЕННЯ ПОЛІГАРМОНІЙНИХ ОПЕРАТОРІВ

СПИСОК ЛІТЕРАТУРИ

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


• 2. 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. https://doi. org/10.1016/.


• 3. 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. https://doi.org/10.1007/.


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


• 5. 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.


• 6. 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/.


• 7. 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. https://doi.org/10.3390/.


• 8. 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/.


• 9. 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/.


• 10. 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. https://doi.org/10.1007/.


• 11. 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/.


• 12. Kharkevych Yu.I., Kal’chuk I.V. Approximation of (ψ, β )–differentiable functions by Weierstrass integrals. Ukrainian Mathematical Journal. 2007. Vol. 59, N 7. P. 1059–1087. https://doi.org/10.1007/.


• 13. 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. https://doi.org/10.1007/.


• 14. 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. https://doi.org/10.15330/.


• 15. 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. https://doi.org/10.1007/.


• 16. 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/.


• 17. 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/.


• 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/.


• 19. Kharkevych Yu.I., Kal’chuk I.V. Asymptotics of the values of approximations in the mean for classes of differentiable functions by using biharmonic Poisson integrals. Ukrainian Mathematical Journal. 2007. Vol. 59, N 8. P. 1224–1237. https://doi.org/10.1007/.


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


• 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/.


• 22. Zhyhallo T.V., Kharkevych Yu.I. Approximation of (ψ, β )–differentiable functions by Poisson integrals in the uniform metric. Ukrainian Mathematical Journal. 2009. Vol. 61, N 11. P. 1757–1779. https://doi.org/10.1007/.


• 23. 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. https://doi.org/10.15330/.


• 24. Zajac 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/.


• 25. Mishchuk A.Yu., Shutovskyi A.M. Optimization properties of generalized Chebyshev–Poisson integrals. Cybernetics and Systems Analysis. 2024. Vol. 60, N 4. P. 613–620. https://doi.org/ 10.1007/.


• 26. Zhyhallo T.V., Kharkevych Yu.I. Approximation of functions from the class C 
  ^ψ _β,∞
  by Poisson integrals in the uniform metric. Ukrainian Mathematical Journal. 2009. Vol. 61, N 12. P. 1893–1914. https://doi.org/10.1007/.


• 27. 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. https://doi.org/10.1007/.


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


• 29. Shutovskyi A.M., Pryt V.V. Optimization characteristics of the operator with delta-like kernel for quasi-smooth functions. Cybernetics and Systems Analysis. 2024. Vol. 60, N 5. P. 792–798. https://doi.org/10.1007/.


• 30. 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. https://doi.org/10.1007/.


• 31. Korenkov M.E., Zajac J., Kharkevych Yu.I. Nevanlinna characteristics and defective values of the Weierstrass zeta function. Ukrainian Mathematical Journal. 2011. Vol. 63, N 5. P. 838–841. https://doi.org/10.1007/.


• 32. 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/.


• 33. 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/.


• 34. 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.


• 35. 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. https://doi.org/10.1134/.