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Trudy Mat. Inst. Steklov., 1985, Volume 172, Pages 187–191 (Mi tm2177)  

This article is cited in 32 scientific papers (total in 33 papers)

On approximation properties of complete orthonormal systems

B. S. Kashin


Full text: PDF file (427 kB)

English version:
Proceedings of the Steklov Institute of Mathematics, 1987, 172, 207–211

Bibliographic databases:
UDC: 517.5

Citation: B. S. Kashin, “On approximation properties of complete orthonormal systems”, Investigations on the theory of functions of several real variables and approximation of functons, Collection of articles. Dedicated to the academician S. M. Nikol'skij on the occasion of his 80th birthday, Trudy Mat. Inst. Steklov., 172, 1985, 187–191; Proc. Steklov Inst. Math., 172 (1987), 207–211

Citation in format AMSBIB
\Bibitem{Kas85}
\by B.~S.~Kashin
\paper On approximation properties of complete orthonormal systems
\inbook Investigations on the theory of functions of several real variables and approximation of functons
\bookinfo Collection of articles. Dedicated to the academician S.\,M.~Nikol'skij on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklov.
\yr 1985
\vol 172
\pages 187--191
\mathnet{http://mi.mathnet.ru/tm2177}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=810427}
\zmath{https://zbmath.org/?q=an:0581.42018|0635.42030}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1987
\vol 172
\pages 207--211


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

    This publication is cited in the following articles:
    1. B. S. Kashin, V. N. Temlyakov, “On best $m$-term approximations and the entropy of sets in the space $L_1$”, Math. Notes, 56:5 (1994), 1137–1157  mathnet  crossref  mathscinet  zmath  isi
    2. Donoho D., “Cart and Best-Ortho-Basis: a Connection”, Ann. Stat., 25:5 (1997), 1870–1911  crossref  mathscinet  zmath  isi
    3. Temlyakov V.N., “Greedy algorithms with regard to multivariate systems with special structure”, Constr. Approx., 16:3 (2000), 399–425  crossref  mathscinet  zmath  isi
    4. B. S. Kashin, “Lower Bounds for $n$-Term Approximations”, Math. Notes, 70:4 (2001), 574–576  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. 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
    6. Donoho D., “Sparse Components of Images and Optimal Atomic Decompositions”, Constr. Approx., 17:3 (2001), 353–382  crossref  mathscinet  zmath  isi  scopus
    7. B. S. Kashin, “Lower Bounds for $n$-Term Approximations of Plane Convex Sets and Related Topics”, Math. Notes, 72:4 (2002), 473–478  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. B. S. Kashin, T. Yu. Kulikova, “A Note on the Approximation Properties of Frames of General Form”, Math. Notes, 72:2 (2002), 281–284  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. Temlyakov V., “Universal Bases and Greedy Algorithms For Anisotropic Function Classes”, Constr. Approx., 18:4 (2002), 529–550  crossref  mathscinet  zmath  isi  scopus
    10. 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
    11. Temlyakov V.N., “Nonlinear methods of approximation”, Found. Comput. Math., 3:1 (2003), 33–107  crossref  mathscinet  zmath  isi
    12. DeVore R., Petrova G., Temlyakov V., “Best Basis Selection For Approximation in l-P”, Found. Comput. Math., 3:2 (2003), 161–185  crossref  mathscinet  zmath  isi  scopus
    13. P. G. Grigor'ev, “On the Orthomassivity of the Set of Characteristic Functions of Convex Sets”, Math. Notes, 75:1 (2004), 140–144  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. Candes E., Donoho D., “New Tight Frames of Curvelets and Optimal Representations of Objects With Piecewise C-2 Singularities”, Commun. Pure Appl. Math., 57:2 (2004), 219–266  crossref  mathscinet  zmath  isi
    15. Dai F., “An Extrapolation Theorem For Nonlinear Approximation and Its Applications”, J. Approx. Theory, 143:2 (2006), 135–149  crossref  mathscinet  zmath  isi  scopus
    16. Dahlke S., Novak E., Sickel W., “Optimal Approximation of Elliptic Problems By Linear and Nonlinear Mappings II”, J. Complex., 22:4 (2006), 549–603  crossref  mathscinet  zmath  isi  elib  scopus
    17. Dahlke S., Novak E., Sickel W., “Optimal Approximation of Elliptic Problems By Linear and Nonlinear Mappings III: Frames”, J. Complex., 23:4-6 (2007), 614–648  crossref  mathscinet  zmath  isi  scopus
    18. Bednorz W., “Greedy Bases Are Best For M-Term Approximation”, Constr. Approx., 28:3 (2008), 265–275  crossref  mathscinet  zmath  isi  scopus
    19. Temlyakov V.N., “Greedy Approximation”, Acta Numerica 2008, Vol 17, Acta Numerica-Series, 17, ed. Iserles A., Cambridge Univ Press, 2008, 235–409  crossref  mathscinet  isi  scopus
    20. Stasyuk S.A., “Approximation of Functions in Severeal Variables From Classes H (P) (Omega) By Polynomials With Respect to the Haar System”, Anal. Math., 35:4 (2009), 257–271  crossref  mathscinet  zmath  isi  elib
    21. A. I. Stepanets, A. L. Shidlich, “Extremal problems for integrals of non-negative functions”, Izv. Math., 74:3 (2010), 607–660  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    22. Proc. Steklov Inst. Math., 269 (2010), 247–258  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    23. G. A. Akishev, “O tochnosti otsenok nailuchshego $M$-chlennogo priblizheniya klassa Besova”, Sib. elektron. matem. izv., 7 (2010), 255–274  mathnet  elib
    24. 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  isi
    25. 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
    26. 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
    27. Meng Qingmin, Jiang Yanjie, “Representation and M-Term Approximation For Anisotropic Besov Classes”, J. Math. Anal. Appl., 409:2 (2014), 834–845  crossref  mathscinet  zmath  isi  scopus
    28. 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
    29. 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
    30. Yuan M., Yang B., Ma Y., Zhang J., Zhang R., Zhang C., “Compressed Sensing Mri Reconstruction From Highly Undersampled K-Space Data Using Nonsubsampled Shearlet Transform Sparsity Prior”, Math. Probl. Eng., 2015, 615439  crossref  isi  scopus
    31. Akishev G., “on M-Term Approximations of the Nikol'Skii - Besov Class”, Hacet. J. Math. Stat., 45:2 (2016), 297–310  crossref  mathscinet  zmath  isi  elib  scopus
    32. 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  isi
    33. 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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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