We study the asymptotic behavior of the least upper bounds of the approximations of functions from the classes \( {W}_{\beta}^r{H}^{\alpha } \) by Weierstrass integrals in the uniform metric.
This is a preview of subscription content, log in via an institution to check access.
Access this article
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 1, Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (2002).
N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Nauka, Moscow (1965).
P. P. Korovkin, “On the best approximation of functions from the class Z 2 by linear operators,” Dokl. Akad. Nauk SSSR, 127, No. 3, 143–149 (1959).
L. I. Bausov, “On the approximation of functions from the class Z α by positive methods of summation of the Fourier series,” Usp. Mat. Nauk, 16, No. 3, 143–149 (1961).
L. P. Falaleev, “On the approximation of functions by Abel–Poisson operators,” Sib. Mat. Zh., 42, No. 4, 926–936 (2001).
L. I. Bausov, “Linear methods of summation of the Fourier series by given rectangular matrices. I,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., 46, No. 3, 15–31 (1965).
V. A. Baskakov, “On some properties of Abel–Poisson-type operators,” Mat. Zametki, 17, No. 2, 169–180 (1975).
Yu. I. Kharkevych and I. V. Kal’chuk, “Approximation of (ψ, β)-differentiable functions by Weierstrass integrals,” Ukr. Mat. Zh., 59, No. 7, 953–978 (2007); English translation: Ukr. Math. J., 59, No. 7, 1059–1087 (2007).
I. V. Kal’chuk, “Approximation of (ψ, β)-differentiable functions defined on the real axis by Weierstrass operators,” Ukr. Mat. Zh., 59, No. 9, 1201–1220 (2007); English translation: 59, No. 9, 1342–1363 (2007).
Yu. I. Kharkevych and T. V. Zhyhallo, “Approximation of functions defined on the real axis by operators generated by λ-methods of summation of their Fourier integrals,” Ukr. Mat. Zh., 56, No. 9, 1267–1280 (2004); English translation: 56, No. 9, 1509–1525 (2004).
L. I. Bausov, “Linear methods of summation of Fourier series by given rectangular matrices. II,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., 46, No. 3, 3–17 (1996).
T. V. Zhyhallo and Yu. I. Kharkevych, “Approximation of (ψ, β)-differentiable functions by Poisson integrals in the uniform metric,” Ukr. Mat. Zh., 61, No. 11, 1497–1515 (2009); English translation: 61, No. 11, 1757–1779 (2009).
T. V. Zhyhallo and Yu. I. Kharkevych, “Approximation of functions from the class \( {C}_{\beta}^{\psi } \) by Poisson integrals in the uniform metric,” Ukr. Mat. Zh., 61, No. 12, 1612–1629 (2009); English translation: 61, No. 12, 1893–1914 (2009).
I. V. Kal’chuk and Yu. I. Kharkevych, “Approximating properties of biharmonic Poisson integrals in the classes \( {W}_{\beta}^r{H}^{\alpha } \) ,” Ukr. Mat. Zh., 68, No. 11, 1493–1504 (2016); English translation: 68, No. 11, 1727–1740 (2017).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Fizmatgiz, Moscow (1963).
H. B. Dwight, Tables of Integrals and Other Mathematical Data, Macmillan Company, New York (1961).
A. S. Serdyuk and T. A. Stepaniuk, Uniform Approximations by Fourier Sums on Classes of Generalized Poisson Integrals, Preprint, ArXiv:1603.01891 (2016).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 4, pp. 510–519, April, 2017.
Rights and permissions
About this article
Cite this article
Hrabova, U.Z., Kal’chuk, I.V. & Stepanyuk, T.A. Approximation of Functions from the Classes \( {W}_{\beta}^r{H}^{\alpha } \) by Weierstrass Integrals. Ukr Math J 69, 598–608 (2017). https://doi.org/10.1007/s11253-017-1383-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-017-1383-x