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Mat. Zametki, 1978, Volume 23, Issue 2, Pages 197–212 (Mi mz8133)  

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

Approximation by Fourier sums of classes of functions with several bounded derivatives

È. M. Galeev

M. V. Lomonosov Moscow State University

Abstract: An ordered estimate is obtained for the approximation by Fourier sums, in the metric $\widetilde{\mathscr L}$, $q=(q_1,…,q_n)$, $1<q_<\infty$, $j=1,…,n$, of classes of periodic functions of several variables with zero means with respect to all their arguments, having $m$ mixed derivatives of order $\alpha^1,…,\alpha_i^m$, $\alpha^i\in R^n$. which are bounded in the metrics of$\widetilde{\mathscr L}_{p^1},…,\widetilde{\mathscr L}_{p^m}$, $p^i=(p_1^i,…,p_n^i)$, $1<p_j^i<\infty$, $i=1,…,m$, $j=1,…,n$ by the constants $\beta_1,…,\beta_m$, respectively.

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English version:
Mathematical Notes, 1978, 23:2, 109–117

Bibliographic databases:

UDC: 517.5
Received: 10.06.1976

Citation: È. M. Galeev, “Approximation by Fourier sums of classes of functions with several bounded derivatives”, Mat. Zametki, 23:2 (1978), 197–212; Math. Notes, 23:2 (1978), 109–117

Citation in format AMSBIB
\by \`E.~M.~Galeev
\paper Approximation by Fourier sums of classes of functions with several bounded derivatives
\jour Mat. Zametki
\yr 1978
\vol 23
\issue 2
\pages 197--212
\jour Math. Notes
\yr 1978
\vol 23
\issue 2
\pages 109--117

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    This publication is cited in the following articles:
    1. V. A. Ivanov, “A problem on inequalities for norms of differential operators on homogeneous spaces”, Russian Math. Surveys, 35:5 (1980), 255–256  mathnet  crossref  mathscinet  zmath  adsnasa
    2. È. M. Galeev, “Some estimates for the diameters of the intersection of classes of functions”, Russian Math. Surveys, 37:4 (1982), 115–116  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. N. Temlyakov, “Approximation of functions with a bounded mixed difference by trigonometric polynomials, and the widths of some classes of functions”, Math. USSR-Izv., 20:1 (1983), 173–187  mathnet  crossref  mathscinet  zmath
    4. È. M. Galeev, “Order estimates of derivatives of the multidimensional periodic Dirichlet $\alpha$-kernel in a mixed norm”, Math. USSR-Sb., 45:1 (1983), 31–43  mathnet  crossref  mathscinet  zmath
    5. Ðinh Dung, “The approximation of classes of periodic functions of many variables”, Russian Math. Surveys, 38:6 (1983), 117–118  mathnet  crossref  mathscinet  zmath  isi
    6. V. N. Temlyakov, “Approximation of periodic functions of several variables by trigonometric polynomials, and widths of some classes of functions”, Math. USSR-Izv., 27:2 (1986), 285–322  mathnet  crossref  mathscinet  zmath
    7. È. M. Galeev, “Kolmogorov widths in the space $\widetilde L_q$ of the classes $\widetilde W_p^{\overline\alpha}$ and $\widetilde H_p^{\overline\alpha}$ of periodic functions of several variables”, Math. USSR-Izv., 27:2 (1986), 219–237  mathnet  crossref  mathscinet  zmath
    8. Ðinh Dung, “Approximation by trigonometric polynomials of functions of several variables on the torus”, Math. USSR-Sb., 59:1 (1988), 247–267  mathnet  crossref  mathscinet  zmath
    9. È. M. Galeev, “Kolmogorov widths of classes of periodic functions of one and several variables”, Math. USSR-Izv., 36:2 (1991), 435–448  mathnet  crossref  mathscinet  zmath  adsnasa
    10. E. M. Galeev, “O vlozhenii i priblizhenii peresecheniya mnozhestv i funktsionalnykh klassov”, Vladikavk. matem. zhurn., 6:4 (2004), 25–30  mathnet  mathscinet  zmath  elib
    11. G. Akishev, “O poryadkakh priblizheniya klassov gladkikh funktsii v prostranstvakh Lebega so smeshannoi normoi”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 148, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2006, 5–17  mathnet  zmath
    12. E. M. Skorikov, “The information Kolmogorov width and some exact inequalities between widths”, Izv. Math., 71:3 (2007), 603–627  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. A. A. Vasil'eva, “Kolmogorov Widths of Weighted Sobolev Classes on Closed Intervals”, Math. Notes, 84:5 (2008), 631–635  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    14. E. M. Galeev, “Poperechniki funktsionalnykh klassov i konechnomernykh mnozhestv”, Vladikavk. matem. zhurn., 13:2 (2011), 3–14  mathnet  elib
    15. Pomahiok A.C., “Diameters and Best Approximation of the Classes B-P(R) of Periodic Functions of Several Variables”, Anal. Math., 37:3 (2011), 181–213  crossref  isi
    16. N. N. Pustovoitov, “Approximation of periodic functions in the classes $H_q^\Omega$ by linear methods”, Sb. Math., 203:1 (2012), 88–110  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. Vasil'eva A.A., “Kolmogorov and Linear Widths of the Weighted Besov Classes with Singularity at the Origin”, J. Approx. Theory, 167 (2013), 1–41  crossref  isi
    18. A. A. Vasil'eva, “Widths of weighted Sobolev classes on a John domain”, Proc. Steklov Inst. Math., 280 (2013), 91–119  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    19. G. A. Akishev, “Otsenki nailuchshikh priblizhenii funktsii klassa Nikolskogo - Besova v prostranstve Lorentsa trigonometricheskimi polinomami”, Tr. IMM UrO RAN, 26, no. 2, 2020, 5–27  mathnet  crossref  elib
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