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Mat. Zametki, 1994, Volume 56, Issue 5, Pages 57–86 (Mi mz2288)  

This article is cited in 47 scientific papers (total in 48 papers)

On best $m$-term approximations and the entropy of sets in the space $L_1$

B. S. Kashina, V. N. Temlyakovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b University of South Carolina

Full text: PDF file (2775 kB)
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English version:
Mathematical Notes, 1994, 56:5, 1137–1157

Bibliographic databases:

UDC: 517.5
Received: 28.04.1994

Citation: B. S. Kashin, V. N. Temlyakov, “On best $m$-term approximations and the entropy of sets in the space $L_1$”, Mat. Zametki, 56:5 (1994), 57–86; Math. Notes, 56:5 (1994), 1137–1157

Citation in format AMSBIB
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\by B.~S.~Kashin, V.~N.~Temlyakov
\paper On best $m$-term approximations and the entropy of sets in the space $L_1$
\jour Mat. Zametki
\yr 1994
\vol 56
\issue 5
\pages 57--86
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\zmath{https://zbmath.org/?q=an:0836.41008}
\transl
\jour Math. Notes
\yr 1994
\vol 56
\issue 5
\pages 1137--1157
\crossref{https://doi.org/10.1007/BF02274662}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. B. S. Kashin, V. N. Temlyakov, “Estimate of approximate characteristics for classes of functions with bounded mixed derivative”, Math. Notes, 58:6 (1995), 1340–1342  mathnet  crossref  mathscinet  zmath  isi
    2. M. A. Skopina, “On the norms of polynomials in systems of periodic wavelets in the spaces $L_p$”, Math. Notes, 59:5 (1996), 565–568  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Novak E., “on the Power of Adaption”, J. Complex., 12:3 (1996), 199–237  crossref  mathscinet  zmath  isi  scopus
    4. DeVore R., Temlyakov V., “Nonlinear Approximation in Finite-Dimensional Spaces”, J. Complex., 13:4 (1997), 489–508  crossref  mathscinet  zmath  isi  scopus
    5. Donoho D., “Cart and Best-Ortho-Basis: a Connection”, Ann. Stat., 25:5 (1997), 1870–1911  crossref  mathscinet  zmath  isi
    6. V. N. Temlyakov, “Nonlinear Kolmogorov widths”, Math. Notes, 63:6 (1998), 785–795  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. B. S. Kashin, V. N. Temlyakov, “On a certain norm and related applications”, Math. Notes, 64:4 (1998), 551–554  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Belinsky E., “Estimates of Entropy Numbers and Gaussian Measures For Classes of Functions With Bounded Mixed Derivative”, J. Approx. Theory, 93:1 (1998), 114–127  crossref  mathscinet  zmath  isi
    9. Kushpel A., Levesley J., Wilderotter K., “on the Asymptotically Optimal Rate of Approximation of Multiplier Operators From l-P Into l-Q”, Constr. Approx., 14:2 (1998), 169–185  crossref  mathscinet  zmath  isi
    10. È. S. Belinskii, “Interpolation and integral norms of hyperbolic polynomials”, Math. Notes, 66:1 (1999), 16–23  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. Temlyakov V.N., “Greedy algorithms with regard to multivariate systems with special structure”, Constr. Approx., 16:3 (2000), 399–425  crossref  mathscinet  zmath  isi
    12. Dinh Dung, “Continuous algorithms in $n$-term approximation and non-linear widths”, J. Approx. Theory, 102:2 (2000), 217–242  crossref  mathscinet  zmath  isi
    13. Andrianov A., “Nonlinear Haar Approximation of Functions with Bounded Mixed Derivative”, Wavelet Analysis and Multiresolution Methods, Proceedings, Lecture Notes in Pure and Applied Mathematics, 212, ed. He T., Marcel Dekker, 2000, 27–47  isi
    14. Temlyakov V., “Weak Greedy Algorithms”, Adv. Comput. Math., 12:2-3 (2000), 213–227  crossref  mathscinet  zmath  isi
    15. B. S. Kashin, “Lower Bounds for $n$-Term Approximations”, Math. Notes, 70:4 (2001), 574–576  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. Maiorov V., Meir R., “Lower Bounds For Multivariate Approximation By Affine-Invariant Dictionaries”, IEEE Trans. Inf. Theory, 47:4 (2001), 1569–1575  crossref  mathscinet  zmath  isi  scopus
    17. Donoho D., “Sparse Components of Images and Optimal Atomic Decompositions”, Constr. Approx., 17:3 (2001), 353–382  crossref  mathscinet  zmath  isi  scopus
    18. A. S. Romanyuk, “Approximation of Classes of Periodic Functions in Several Variables”, Math. Notes, 71:1 (2002), 98–109  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    19. Temlyakov V.N., “Universal bases and greedy algorithms for anisotropic function classes”, Constr. Approx., 18:4 (2002), 529–550  crossref  mathscinet  zmath  isi
    20. A. S. Romanyuk, “Best $M$-term trigonometric approximations of Besov classes of periodic functions of several variables”, Izv. Math., 67:2 (2003), 265–302  mathnet  crossref  crossref  mathscinet  zmath  isi
    21. Temlyakov V.N., “Nonlinear methods of approximation”, Found. Comput. Math., 3:1 (2003), 33–107  crossref  mathscinet  zmath  isi
    22. Lutoborski A., Temlyakov V., “Vector Greedy Algorithms”, J. Complex., 19:4 (2003), 458–473  crossref  mathscinet  zmath  isi  scopus
    23. Xu Y., Zou Q., “Tree Wavelet Approximations With Applications”, Sci. China Ser. A-Math., 48:5 (2005), 680–702  crossref  mathscinet  zmath  isi  scopus
    24. 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
    25. Leviatan D., Temlyakov V., “Simultaneous Approximation By Greedy Algorithms”, Adv. Comput. Math., 25:1-3 (2006), 73–90  crossref  mathscinet  zmath  isi  scopus
    26. Kazemi F.M., Samadi S., Poorreza H.R., Akbarzadeh-T M.-R., “Vehicle Recognition Using Curvelet Transform and Svm”, International Conference on Information Technology, Proceedings, ed. Latifi S., IEEE Computer Soc, 2007, 516+  isi
    27. Konohrai A.F., Stasyuk S.A., “Best M-Term Trigonometric Approximations of the Classes B-P,Theta(Omega) of Periodic Functions of Many Variables in the Space Lq”, Ukr. Math. J., 60:9 (2008), 1396–1417  crossref  mathscinet  isi  elib
    28. Kazemi F.M., Izadian J., Moravejian R., Kazemi E.M., “Numeral Recognition Using Curvelet Transform”, 2008 IEEE/Acs International Conference on Computer Systems and Applications, Vols 1-3, International Conference on Computer Systems and Applications, IEEE, 2008, 606–612  crossref  isi  scopus
    29. Kazemi F.M., Pourreza H.R., Moravejian R., Kazemi E.M., “Vehicle Recognition Using Curvelet Transform and Thresholding”, Advances in Computer and Informatiom Sciences and Engineering, ed. Sobh T., Springer, 2008, 142+  crossref  isi  scopus
    30. Stasyuk S.A., “Approximation of functions of several variables from the classes $H_p^\Omega$ by polynomials in the Haar system”, Anal. Math., 35:4 (2009), 257–271  crossref  mathscinet  zmath  isi
    31. Voitenko S.P., “Best $M$-Term trigonometric approximations of the classes $B_{p,\theta}^\Omega$ of periodic functions of many variables”, Ukrainian Math. J., 61:9 (2009), 1404–1416  crossref  isi
    32. Proc. Steklov Inst. Math., 269 (2010), 247–258  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    33. G. A. Akishev, “O tochnosti otsenok nailuchshego $M$-chlennogo priblizheniya klassa Besova”, Sib. elektron. matem. izv., 7 (2010), 255–274  mathnet  elib
    34. Romanyuk A.S., Romanyuk V.S., “ASYMPTOTIC ESTIMATES FOR THE BEST TRIGONOMETRIC AND BILINEAR APPROXIMATIONS OF CLASSES OF FUNCTIONS OF SEVERAL VARIABLES”, Ukrainian Math J, 62:4 (2010), 612–629  crossref  isi
    35. Duan L., “the Best M-Term Approximations on Generalized Besov Classes M Bq,Theta(Omega) With Regard to Orthogonal Dictionaries”, J. Approx. Theory, 162:11 (2010), 1964–1981  crossref  mathscinet  zmath  isi  elib  scopus
    36. Stasyuk S.A., “Best M-Term Trigonometric Approximation For the Classes Bp,Theta(R) of Functions of Low Smoothness”, Ukr. Math. J., 62:1 (2010), 114–122  crossref  mathscinet  zmath  isi  elib
    37. Li R.S., Liu Y.P., “Best M-Term One-Sided Trigonometric Approximation of Some Function Classes Defined By a Kind of Multipliers”, Acta. Math. Sin.-English Ser., 26:5 (2010), 975–984  crossref  mathscinet  zmath  isi  scopus
    38. O. V. Besov, S. V. Bochkarev, B. I. Golubov, A. A. Gonchar, M. I. D'yachenko, V. V. Kozlov, S. V. Konyagin, Yu. V. Malykhin, S. M. Nikol'skii, M. K. Potapov, V. A. Sadovnichii, S. A. Telyakovskii, “Boris Sergeevich Kashin (on his 60th birthday)”, Russian Math. Surveys, 66:4 (2011), 825–828  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    39. 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  elib  scopus
    40. 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
    41. 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
    42. D. B. Bazarkhanov, “Nonlinear trigonometric approximations of multivariate function classes”, Proc. Steklov Inst. Math., 293 (2016), 2–36  mathnet  crossref  crossref  mathscinet  isi  elib
    43. 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, eds. Qian T., Rodino L., Springer, 2016, 183–215  crossref  mathscinet  isi  scopus
    44. Romanyuk A.S., “Estimation of the Entropy Numbers and Kolmogorov Widths For the Nikol'Skii-Besov Classes of Periodic Functions of Many Variables”, Ukr. Math. J., 67:11 (2016), 1739–1757  crossref  mathscinet  isi  elib
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    47. Romanyuk A.S., “Trigonometric and Linear Widths For the Classes of Periodic Multivariate Functions”, Ukr. Math. J., 69:5 (2017), 782–795  crossref  isi
    48. B. S. Kashin, “Ob otsenkakh snizu $m$-chlennykh priblizhenii v metrike diskretnogo prostranstva $L_n^0$”, UMN, 76:5(461) (2021), 199–200  mathnet  crossref
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