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Journal of Automation and Information Sciences

年間 12 号発行

ISSN 印刷: 1064-2315

ISSN オンライン: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

Indexed in

On Approximation of the Quasi-Smooth Functions by Their Poisson Type Integrals

巻 49, 発行 10, 2017, pp. 74-81
DOI: 10.1615/JAutomatInfScien.v49.i10.80
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要約

Consideration is given to the matter of approximation of quasi-smooth functions by their Poison type integrals. The solution of this problem finds its application in various branches of applied mathematics, in particular, in the theory of forecasting and decision making, the mathematical modeling of complex technical and economic systems, the analysis of optimal control problems, the construction of numerical algorithms, and the information compression. Here we found the complete asymptotic expansions in powers (1-r) of the exact upper bounds of deviations of quasi-smooth functions from their Poisson type integrals in the uniform metrics.

によって引用された
  1. Kalchuk I., Kharkevych Yu., ON THE APPROXIMATION ON AVERAGE OF THE HOLDER CLASS FUNCTION BY THEIR GENERALIZED POISSON INTEGRALS, Bukovinian Mathematical Journal, 6, 1-2, 2018. Crossref

  2. Shutovskyi Arsen M., Sakhnyuk Vasyl Ye., Representation of Weierstrass integral via Poisson integrals, Journal of Mathematical Sciences, 259, 1, 2021. Crossref

  3. Sobchuk Valentyn, Kal'chuk Inna, Kharkevych Galyna, Laptiev Oleksandr, Kharkevych Yurii, Makarchuk Andriy, Solving the Problem of Convergence of the Results of Analog Signals Conversion in the Process of Aircraft Control, 2021 IEEE 6th International Conference on Actual Problems of Unmanned Aerial Vehicles Development (APUAVD), 2021. Crossref

  4. Makarchuk Andriy, Kal'chuk Inna, Kharkevych Yurii, Voloshyna Tetiana, Usage of Fourier Transformation in Theoretical Studying of Signals in Data Transmission, 2020 IEEE 2nd International Conference on Advanced Trends in Information Theory (ATIT), 2020. Crossref

  5. Kal’chuk Inna, Kharkevych Yurii, Approximation Properties of the Generalized Abel-Poisson Integrals on the Weyl-Nagy Classes, Axioms, 11, 4, 2022. Crossref

  6. Sobchuk Valentyn, Kal'Chuk Inna, Kharkevych Yurii, Kharkevych Galyna, Estimations of the Convergence Rate of the Fourier Transformation for Data Processing Efficiency Improvement, 2021 IEEE 3rd International Conference on Advanced Trends in Information Theory (ATIT), 2021. Crossref

  7. Shutovskyi Arsen, Sakhnyuk Vasyl, Representation of Weierstrass integral via Poisson integrals, Ukrainian Mathematical Bulletin, 18, 3, 2021. Crossref

  8. Makarchuk Andriy, Kal'Chuk Inna, Kharkevych Yurii, Salnikova Svitlana, Biharmonic Equations Integrals Application Features at Signals Restoration by Means of Interpolation Polynomials, 2021 IEEE 3rd International Conference on Advanced Trends in Information Theory (ATIT), 2021. Crossref

  9. Shvai Olga, Pozharska Kateryna, On some approximation properties of Gauss-Weierstrass singular operators, Journal of Mathematical Sciences, 260, 5, 2022. Crossref

  10. Kharkevych Galyna, Kharkevych Yurii, Kal'chuk Inna, Sobchuk Valentyn, Usage of Fourier transformation theory in machine translation, 2020 IEEE 2nd International Conference on Advanced Trends in Information Theory (ATIT), 2020. Crossref

  11. Kal'chuk I. V., Kharkevych Yu. I., Наближення класів W β , ∞ r узагальненими інтегралами Абеля – Пуассона, Ukrains’kyi Matematychnyi Zhurnal, 74, 4, 2022. Crossref

  12. Shvai Olga, Pozharska Kateryna, On some approximation properties of Gauss-Weierstrass singular operators, Ukrainian Mathematical Bulletin, 18, 4, 2021. Crossref

  13. Kharkevych Yu. I., On Some Asymptotic Properties of Solutions to Biharmonic Equations, Cybernetics and Systems Analysis, 58, 2, 2022. Crossref

  14. Hrabova Ulyna, Tovkach Roman, On a boundary properties of functions from a class Hp(p ≥ 1), Journal of Mathematical Sciences, 264, 4, 2022. Crossref

  15. Shutovskyi Arsen M., Sakhnyuk Vasyl Ye., Taylor Series of Biharmonic Poisson Integral for Upper Half-Plane, Journal of Mathematical Sciences, 268, 2, 2022. Crossref

  16. Kal’chuk I. V., Kharkevych Yu. I., Approximation of the Classes $$ {W}_{\beta, \infty}^R $$ by Generalized Abel–Poisson Integrals, Ukrainian Mathematical Journal, 74, 4, 2022. Crossref

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