A. S. Romanyuk, “Best Trigonometric Approximations for Some Classes of Periodic Functions of Several Variables in the Uniform Metric”, Mat. Zametki, 82:2 (2007), 247–261; Math. Notes, 82:2 (2007), 216

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Matematicheskie Zametki, 2007, Volume 82, Issue 2, Pages 247–261
DOI: https://doi.org/10.4213/mzm3797 (Mi mzm3797)

This article is cited in 22 scientific papers (total in 22 papers)

Best Trigonometric Approximations for Some Classes of Periodic Functions of Several Variables in the Uniform Metric

A. S. Romanyuk

Institute of Mathematics, Ukrainian National Academy of Sciences

Full-text PDF (536 kB) Citations (22)

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DOI: https://doi.org/10.4213/mzm3797

Abstract: We study best

M

$M$ -term trigonometric approximations and best orthogonal trigonometric approximations for the classes

B_{p, θ}^{r}

$B^r_{p,\theta}$ and

W_{p, α}^{r}

$W^r_{p,\alpha}$ of periodic functions of several variables in the uniform metric.

Keywords: best trigonometric approximation, the classes

B_{p, θ}^{r}

$B^r_{p,\theta}$ and

W_{p, α}^{r}

$W^r_{p,\alpha}$ of periodic functions, Minkowski's inequality, Hölder's inequality, Vallée-Poussin kernel.

Received: 28.03.2005
Revised: 17.11.2006

English version:
Mathematical Notes, 2007, Volume 82, Issue 2, Pages 216–228
DOI: https://doi.org/10.1134/S0001434607070279

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: A. S. Romanyuk, “Best Trigonometric Approximations for Some Classes of Periodic Functions of Several Variables in the Uniform Metric”, Mat. Zametki, 82:2 (2007), 247–261; Math. Notes, 82:2 (2007), 216–228

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm3797

https://doi.org/10.4213/mzm3797

https://www.mathnet.ru/eng/mzm/v82/i2/p247

This publication is cited in the following 22 articles:

G. Akishev, “Estimates of $M$ –term approximations of functions of several variables in the Lorentz space by a constructive method”, Eurasian Math. J., 15:2 (2024), 8–32
Svitlana Hembars'ka, Ihor Romanyuk, Oksana Fedunyk-Yaremchuk, “Characteristics of the linear and nonlinear approximations of the Nikol'skii-Besov-type classes of periodic functions of several variables”, UMB, 20:2 (2023), 161
G. A. Akishev, “O nailuchshikh $M$ -chlennykh priblizheniyakh funktsii klassa Nikolskogo – Besova v prostranstve Lorentsa”, Tr. IMM UrO RAN, 28, no. 1, 2022, 7–26
S. B. Hembars'ka, P. V. Zaderei, “Naikraschі ortogonalnі trigonometrichnі nablizhennya klasіv tipu Nіkolskogo – Bєsova perіodichnikh funktsіi u prostorі
B
∞ ,1”, Ukr. Mat. Zhurn., 74:6 (2022), 772
A. S. Romanyuk, S. Ya. Yanchenko, “Approximation of the Classes of Periodic Functions of One and Many Variables from the Nikol'skii–Besov and Sobolev Spaces”, Ukr Math J, 74:6 (2022), 967
S. B. Hembars'ka, P. V. Zaderei, “Best Orthogonal Trigonometric Approximations of the Nikol'skii–Besov-Type Classes of Periodic Functions in the Space B∞,1”, Ukr Math J, 74:6 (2022), 883
A. S. Romanyuk, S. Ya. Yanchenko, “Nablizhennya klasіv perіodichnikh funktsіi odnієï ta bagatokh zmіnnikh іz prostorіv Nіkolskogo – Bєsova ta Sobolєva”, Ukr. Mat. Zhurn., 74:6 (2022), 844
V. K. Nguyen, V. D. Nguyen, “Best n-Term Approximation of Diagonal Operators and Application to Function Spaces with Mixed Smoothness”, Anal Math, 48:4 (2022), 1127
Romanyuk A.S. Romanyuk V.S., “Estimation of Some Approximating Characteristics of the Classes of Periodic Functions of One and Many Variables”, Ukr. Math. J., 71:8 (2020), 1257–1272
Yanchenko S.Ya. Radchenko O.Ya., “Approximating Characteristics of the Nikol'Skii-Besov Classes (S1,Theta B)-B-R(R-D)”, Ukr. Math. J., 71:10 (2020), 1608–1626
Tetiana A. Stepanyuk, Trigonometric Sums and Their Applications, 2020, 273
Mykhailo V. Hembars'kyi, Svitlana B. Hembars'ka, “Approximate characteristics of the classes ${B}_{p,\theta}^{\Omega}$ of periodic functions of one variable and many ones”, J Math Sci, 242:6 (2019), 820
Mykhailo Hembars'kyi, Svitlana Hembars'ka, “Approximate characteristics of the classes $B_{p,\theta}^{\Omega}$ of periodic functions of one variable and many ones”, UMB, 16:1 (2019), 88
D. B. Bazarkhanov, “Nonlinear trigonometric approximations of multivariate function classes”, Proc. Steklov Inst. Math., 293 (2016), 2–36
Shvai K.V., “the Best M-Term Trigonometric Approximations of Classes of (Psi,Beta)-Differentiable Periodic Multivariate Functions in the Space l-Beta,1(Psi)”, J. Numer. Appl. Math., 2:122 (2016), 83–91
Shkapa V.V., “Best Trigonometric and Bilinear Approximations for the Classes of (, )-Differentiable Periodic Functions”, Ukr. Math. J., 68:3 (2016), 433–447
Serdyuk A.S., Stepanyuk T.A., “Order Estimates For the Best Orthogonal Trigonometric Approximations of the Classes of Convolutions of Periodic Functions of Low Smoothness”, Ukr. Math. J., 67:7 (2015), 1038–1061
Sergei A. Stasyuk, “Approximations of the classes MB p,θ r of periodic functions of several variables by polynomials according to the Haar system”, J Math Sci, 210:1 (2015), 76
A.S. Serdyuk, T.A. Stepaniuk, “Estimates of the best orthogonal trigonometric approximations of the classes of convolutions of periodic functions of not high smoothness”, Dopov. Nac. akad. nauk Ukr., 2015, no. 7, 13
D. B. Bazarkhanov, “Nonlinear approximations of classes of periodic functions of many variables”, Proc. Steklov Inst. Math., 284 (2014), 2–31

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

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