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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 2, Pages 61–100 (Mi izv427)  

This article is cited in 28 scientific papers (total in 28 papers)

Best $M$-term trigonometric approximations of Besov classes of periodic functions of several variables

A. S. Romanyuk

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We obtain order-exact estimates for the best $M$-term trigonometric approximations of the Besov classes $B_{p,\theta}^r$ of periodic functions of several variables in $L_q$ with certain relations between $p$ and $q$.


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English version:
Izvestiya: Mathematics, 2003, 67:2, 265–302

Bibliographic databases:

UDC: 517.5
MSC: 42B99, 41A46, 41A50
Received: 27.07.2001

Citation: A. S. Romanyuk, “Best $M$-term trigonometric approximations of Besov classes of periodic functions of several variables”, Izv. RAN. Ser. Mat., 67:2 (2003), 61–100; Izv. Math., 67:2 (2003), 265–302

Citation in format AMSBIB
\by A.~S.~Romanyuk
\paper Best $M$-term trigonometric approximations of Besov classes of periodic functions of several variables
\jour Izv. RAN. Ser. Mat.
\yr 2003
\vol 67
\issue 2
\pages 61--100
\jour Izv. Math.
\yr 2003
\vol 67
\issue 2
\pages 265--302

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    This publication is cited in the following articles:
    1. A. S. Romanyuk, “Kolmogorov and trigonometric widths of the Besov classes $B^r_{p,\theta}$ of multivariate periodic functions”, Sb. Math., 197:1 (2006), 69–93  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. S. Romanyuk, “Bilinear and trigonometric approximations of periodic functions of several variables of Besov classes $B_{p, \theta}^r$”, Izv. Math., 70:2 (2006), 277–306  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. S. Romanyuk, “Best Trigonometric Approximations for Some Classes of Periodic Functions of Several Variables in the Uniform Metric”, Math. Notes, 82:2 (2007), 216–228  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. S. Romanyuk, “Best approximations and widths of classes of periodic functions of several variables”, Sb. Math., 199:2 (2008), 253–275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Ren Suo Li, Yong Ping Liu, “Best m-term one-sided trigonometric approximation of some function classes defined by a kind of multipliers”, Acta Math Sinica, 2009  crossref  mathscinet  isi  scopus
    6. Bazarkhanov D.B., “Estimates for certain approximation characteristics of Nikol'skii-Besov spaces with generalized mixed smoothness”, Dokl. Math., 79:3 (2009), 305–308  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    7. G. A. Akishev, “O tochnosti otsenok nailuchshego $M$-chlennogo priblizheniya klassa Besova”, Sib. elektron. matem. izv., 7 (2010), 255–274  mathnet  elib
    8. Markus Hansen, Winfried Sickel, “Best m-Term Approximation and Sobolev–Besov Spaces of Dominating Mixed Smoothness—the Case of Compact Embeddings”, Constr Approx, 2012  crossref  mathscinet  isi  scopus
    9. Rensuo Li, Yongping Liu, “The Best m-Term One-Sided Approximation of Besov Classes by the Trigonometric Polynomials”, APM, 02:03 (2012), 183  crossref
    10. A. S. Romanyuk, “Best Trigonometric and Bilinear Approximations of Classes of Functions of Several Variables”, Math. Notes, 94:3 (2013), 379–391  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. D. B. Bazarkhanov, “Nonlinear approximations of classes of periodic functions of many variables”, Proc. Steklov Inst. Math., 284 (2014), 2–31  mathnet  crossref  crossref  isi  elib  elib
    12. Stasyuk S.A., “Best M-Term Trigonometric Approximation of Periodic Functions of Several Variables From Nikol'skii-Besov Classes for Small Smoothness”, J. Approx. Theory, 177 (2014), 1–16  crossref  mathscinet  isi  scopus
    13. V. N. Temlyakov, “Constructive sparse trigonometric approximation and other problems for functions with mixed smoothness”, Sb. Math., 206:11 (2015), 1628–1656  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    14. S. A. Stasyuk, “Priblizhenie nekotorykh gladkostnykh klassov periodicheskikh funktsii mnogikh peremennykh polinomami po tenzornoi sisteme Khaara”, Tr. IMM UrO RAN, 21, no. 4, 2015, 251–260  mathnet  mathscinet  elib
    15. D. B. Bazarkhanov, “Nonlinear trigonometric approximations of multivariate function classes”, Proc. Steklov Inst. Math., 293 (2016), 2–36  mathnet  crossref  crossref  mathscinet  isi  elib
    16. S. A. Stasyuk, “Konstruktivnye razrezhennye trigonometricheskie priblizheniya dlya klassov funktsii s nebolshoi smeshannoi gladkostyu”, Tr. IMM UrO RAN, 22, no. 4, 2016, 247–253  mathnet  crossref  mathscinet  elib
    17. Temlyakov V., “Sparse Approximation by Greedy Algorithms”, Mathematical Analysis, Probability and Applications – Plenary Lectures, Springer Proceedings in Mathematics & Statistics, Springer Proceedings in Mathematics & Statistics, 177, ed. Qian T. Rodino L., Springer, 2016, 183–215  crossref  mathscinet  zmath  isi  scopus
    18. 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  isi
    19. Stasyuk S.A., “Best m-Term Trigonometric Approximation for Periodic Functions with Low Mixed Smoothness from the Nikol'skii–Besov-Type Classes”, Ukr. Math. J., 68:7 (2016), 1121–1145  crossref  mathscinet  isi  scopus
    20. Shkapa V.V., “Best Trigonometric and Bilinear Approximations for the Classes of (, )-Differentiable Periodic Functions”, Ukr. Math. J., 68:3 (2016), 433–447  crossref  mathscinet  isi  scopus
    21. Akishev G., “On M-term approximations of the Nikolskii - Besov class”, Hacet. J. Math. Stat., 45:2 (2016), 297–310  crossref  mathscinet  zmath  isi  elib  scopus
    22. Shkapa V.V., “Approximating Characteristics of the Classes L ,p of Periodic Functions in the Space L q”, Ukr. Math. J., 67:8 (2016), 1283–1295  crossref  mathscinet  zmath  isi  elib  scopus
    23. S. A. Stasyuk, “Razrezhennoe trigonometricheskoe priblizhenie klassov Besova funktsii s maloi smeshannoi gladkostyu”, Tr. IMM UrO RAN, 23, no. 3, 2017, 244–252  mathnet  crossref  elib
    24. Akishev G., “Estimations of the Best M - Term Approximations of Functions in the Lorentz Space With Constructive Methods”, Bull. Karaganda Univ-Math., 87:3 (2017), 13–26  mathscinet  isi
    25. Romanyuk A.S., “Trigonometric and Linear Widths For the Classes of Periodic Multivariate Functions”, Ukr. Math. J., 69:5 (2017), 782–795  crossref  mathscinet  isi  scopus
    26. Temlyakov V., “Constructive Sparse Trigonometric Approximation For Functions With Small Mixed Smoothness”, Constr. Approx., 45:3 (2017), 467–495  crossref  mathscinet  zmath  isi  scopus
    27. Romanyuk A.S., “Kolmogorov Widths and Bilinear Approximations of the Classes of Periodic Functions of One and Many Variables”, Ukr. Math. J., 70:2 (2018), 252–265  crossref  mathscinet  isi  scopus
    28. Shvai K.V., “Estimation of the Best Bilinear Approximations For the Classes of (Psi, Beta)-Differentiable Periodic Multivariable Functions”, Ukr. Math. J., 70:4 (2018), 649–660  crossref  mathscinet  isi  scopus
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