Yu. I. Kharkevich, T. A. Stepanyuk, “Approximation Properties of Poisson Integrals for the Classes $C^{\psi}_{\beta}H^{\alpha}$”, Mat. Zametki, 96:6 (2014), 939–952; Math. Notes, 96:6 (2014), 1008

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Matematicheskie Zametki, 2014, Volume 96, Issue 6, Pages 939–952
DOI: https://doi.org/10.4213/mzm9681 (Mi mzm9681)

This article is cited in 19 scientific papers (total in 19 papers)

Approximation Properties of Poisson Integrals for the Classes

C_{β}^{ψ} H^{α}

$C^{\psi}_{\beta}H^{\alpha}$

Yu. I. Kharkevich, T. A. Stepanyuk

Volyn University of Lesya Ukrainka

Full-text PDF (503 kB) Citations (19)

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DOI: https://doi.org/10.4213/mzm9681

Abstract: Questions dealing with the approximation of functions from the classes

C_{β}^{ψ} H^{α}

$C^{\psi}_{\beta}H^{\alpha}$ by Poisson integrals are studied. The Kolmogorov–Nikolskii problem for Poisson integrals for the classes

C_{β}^{ψ} H^{α}

$C^{\psi}_{\beta}H^{\alpha}$ is solved in the uniform metric.

Keywords: approximation of functions, the classes

C_{β}^{ψ} H^{α}

$C^{\psi}_{\beta}H^{\alpha}$ , Poisson integral, Fourier series, Kolmogorov–Nikolskii problem,

(ψ, β)

$(\psi,\beta)$ -derivative.

Received: 27.04.2012
Revised: 27.11.2013

English version:
Mathematical Notes, 2014, Volume 96, Issue 6, Pages 1008–1019
DOI: https://doi.org/10.1134/S0001434614110406

Bibliographic databases:

Document Type: Article

UDC: 517.5

Language: Russian

Citation: Yu. I. Kharkevich, T. A. Stepanyuk, “Approximation Properties of Poisson Integrals for the Classes

C_{β}^{ψ} H^{α}

$C^{\psi}_{\beta}H^{\alpha}$ ”, Mat. Zametki, 96:6 (2014), 939–952; Math. Notes, 96:6 (2014), 1008–1019

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm9681

https://doi.org/10.4213/mzm9681

https://www.mathnet.ru/eng/mzm/v96/i6/p939

This publication is cited in the following 19 articles:

E.T. Karimov, N.E. Tokmagambetov, D.A. Usmonov, “INVERSE-INITIAL PROBLEM FOR TIME-DEGENERATE PDE INVOLVING THE BI-ORDINAL HILFER DERIVATIVE”, KCA, 2024, 133
R. V. Tovkach, V. M. Medvid, “A Necessary Condition for the Convergence of the Fourier Transform”, Cybern Syst Anal, 2024
R.V. Tovkach, V.M. Medvid, “A NECESSARY CONDITION FOR THE CONVERGENCE OF THE FOURIER TRANSFORM”, KCA, 2024, 146
P. G. Potseiko, E. A. Rovba, K. A. Smotritskii, “On the approximation of conjugate functions and their derivatives on the segment by partial sums of Fourier - Chebyshev series”, Zhurn. Belorus. gos. un-ta. Matem. Inf., 2 (2024), 6–18
Oleksandr Laptiev, Ivan Parkhomenko, Andrii Musienko, Andriy Makarchuk, Anton Mishchuk, Denys Shapovalov, 2023 IEEE 4th KhPI Week on Advanced Technology (KhPIWeek), 2023, 1
Yu. I. Kharkevych, O. G. Khanin, “Asymptotic Properties of the Solutions of Higher-Order Differential Equations on Generalized Hölder Classes”, Cybern Syst Anal, 59:4 (2023), 633
Ulyana Z. Hrabova, Inna V. Kal'chuk, “Approximation of Classes $ {C}_{\beta, \infty}^{\psi } $ by Three-Harmonic Poisson Integrals in Uniform Metric (Low Smoothness)”, J Math Sci, 268:2 (2022), 178
Ulyana Z. Hrabova, Inna V. Kal'chuk, Leontii I. Filozof, “Approximative properties of the three-harmonic Poisson integrals on the classes $ {W}_{\beta}^r{H}^{\alpha } $”, J Math Sci, 254:3 (2021), 397
Kal'chuk V I. Kharkevych I Yu. Pozharska V K., “Asymptotics of Approximation of Functions By Conjugate Poisson Integrals”, Carpathian Math. Publ., 12:1 (2020), 138–147
Abdullayev F.G. Bushev D.M. Kyzy M.I. Kharkevych Yu.I., “Isometry of the Subspaces of Solutions of Systems of Differential Equations to the Spaces of Real Functions”, Ukr. Math. J., 71:8 (2020), 1153–1172
Abdullayev F.G. Kharkevych Yu.I., “Approximation of the Classes (C Beta H Alpha)-H-Psi By Biharmonic Poisson Integrals”, Ukr. Math. J., 72:1 (2020), 21–38
Ulyana Hrabova, Inna Kal'chuk, Leontii Filozof, “Approximative properties of the three-harmonic Poisson integrals on the classes $W^{r}_{\beta}H^{\alpha}$.”, UMB, 17:4 (2020), 538
U. Z. Hrabova, I. V. Kal'chuk, “Approximation of the classes w-beta infinity(r) by three-harmonic Poisson integrals”, Carpathian Math. Publ., 11:2 (2019), 321–334
I. V. Kal'chuk, Yu. I. Kharkevych, “Complete asymptotics of the approximation of function from the Sobolev classes by the Poisson integrals”, Acta Comment. Univ. Tartu. Math., 22:1 (2018), 23–36
D. N. Bushev, Yu. I. Kharkevich, “Finding Solution Subspaces of the Laplace and Heat Equations Isometric to Spaces of Real Functions, and Some of Their Applications”, Math. Notes, 103:6 (2018), 869–880
U. Z. Hrabova, I. V. Kal'chuk, T. A. Stepanyuk, “On approximation of the classes $W^r_{\beta} H^{\alpha}$ by biharmonic Poisson integrals”, Ukr. Math. J., 70:5 (2018), 719–729
Yu. I. Kharkevych, K. V. Pozharska, “Asymptotics of approximation of conjugate functions by Poisson integrals”, Acta Comment. Univ. Tartu. Math., 22:2 (2018), 235–243
Uliana Z. Grabova, Inna V. Kal'chuk, Tetiana A. Stepaniuk, “Approximative properties of the Weierstrass integrals on the classes W β r H α $ {W}_{\beta}^r{H}^{\alpha } $”, J Math Sci, 231:1 (2018), 41
I. V. Kal'chuk, Yu. I. Kharkevych, “Approximative properties of biharmonic Poisson integrals on the classes $W^r_\beta H^\alpha$”, Ukr. Math. J., 68:11 (2017), 1727–1740

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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