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Trudy Mat. Inst. Steklov., 1980, Volume 145, Pages 111–116 (Mi tm2535)  

This article is cited in 27 scientific papers (total in 28 papers)

Some properties of the space of trigonometric polynomials with a uniform norm

B. S. Kashin

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English version:
Proceedings of the Steklov Institute of Mathematics, 1981, 145, 121–127

Bibliographic databases:
UDC: 517.5

Citation: B. S. Kashin, “Some properties of the space of trigonometric polynomials with a uniform norm”, Approximation of functions by polynomials and splines, Work collection, Trudy Mat. Inst. Steklov., 145, 1980, 111–116; Proc. Steklov Inst. Math., 145 (1981), 121–127

Citation in format AMSBIB
\by B.~S.~Kashin
\paper Some properties of the space of trigonometric polynomials with a~uniform norm
\inbook Approximation of functions by polynomials and splines
\bookinfo Work collection
\serial Trudy Mat. Inst. Steklov.
\yr 1980
\vol 145
\pages 111--116
\jour Proc. Steklov Inst. Math.
\yr 1981
\vol 145
\pages 121--127

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    This publication is cited in the following articles:
    1. Kasin B., “Diameters of Sobolev Classes of Small Order Smoothness”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1981, no. 5, 50–54  mathscinet  isi
    2. Kosheleva G., “the Properties of the Space U(0, 2-Pi)”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1984, no. 5, 20–25  mathscinet  zmath  isi
    3. B. S. Kashin, “On homogeneous polynomials of several variables on the complex sphere”, Math. USSR-Sb., 54:2 (1986), 409–414  mathnet  crossref  mathscinet  zmath
    4. Koriogin A., “the Absolute Convergence of Multiple Trigonometric Series With Lacunas”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1985, no. 4, 3–9  mathscinet  isi
    5. E. D. Gluskin, “Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces”, Math. USSR-Sb., 64:1 (1989), 85–96  mathnet  crossref  mathscinet  zmath  isi
    6. Temliakov V.N., “On estimates of $\epsilon$-entropy and widths of classes of functions with a bounded mixed derivative or difference”, Dokl. AN SSSR, 301:2 (1988), 288–291  mathnet  isi
    7. V. N. Temlyakov, “On a way of obtaining lower estimates for the errors of quadrature formulas”, Math. USSR-Sb., 71:1 (1992), 247–257  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. Hajela D., “on Polynomials With Low Peak Signal to Power (l-Infinity-Norm to l2-Norm) Ratios and Theorems of Kashin and Spencer”, Stud. Appl. Math., 87:1 (1992), 81–94  crossref  mathscinet  zmath  isi
    9. B. S. Kashin, L. A. Tzafriri, “Random sets of uniform convergence”, Math. Notes, 54:1 (1993), 677–687  mathnet  crossref  mathscinet  zmath  isi  elib
    10. 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
    11. V. N. Temlyakov, “Nonlinear Kolmogorov widths”, Math. Notes, 63:6 (1998), 785–795  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. Kushpel A.K., 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
    13. S. V. Astashkin, “On the selection of subsystems equivalent in distribution to the Rademacher system”, Math. Notes, 66:3 (1999), 384–388  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. Oskolkov K., “Ridge Approximation and Kolmogorov-Nikol'Skii Problem”, Dokl. Akad. Nauk, 368:4 (1999), 445–448  mathnet  mathscinet  zmath  isi
    15. S. V. Astashkin, “Systems of random variables equivalent in distribution to the Rademacher system and $\mathscr K$-closed representability of Banach couples”, Sb. Math., 191:6 (2000), 779–807  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. Kushpel A., “Optimal Approximation on S-D”, J. Complex., 16:2 (2000), 424–458  crossref  mathscinet  zmath  isi  scopus
    17. B. S. Kashin, V. N. Temlyakov, “On a Norm and Approximate Characteristics of Classes of Multivariable Functions”, Journal of Mathematical Sciences, 155:1 (2008), 57–80  mathnet  crossref  mathscinet  zmath  elib
    18. K. I. Oskolkov, “Linear and Nonlinear Methods of Relief Approximation”, Journal of Mathematical Sciences, 155:1 (2008), 129–152  mathnet  crossref  mathscinet  zmath
    19. Konovalov V.N., Leviatan D., Maiorov V.E., “Approximation by polynomials and ridge functions of classes of s-monotone radial functions”, J Approx Theory, 152:1 (2008), 20–51  crossref  isi
    20. S. V. Astashkin, “Rademacher functions in symmetric spaces”, Journal of Mathematical Sciences, 169:6 (2010), 725–886  mathnet  crossref  mathscinet  zmath  elib
    21. Seeger A., Trebels W., “Low Regularity Classes and Entropy Numbers”, Arch. Math., 92:2 (2009), 147–157  crossref  mathscinet  zmath  isi  scopus
    22. 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
    23. Bazarkhanov D.B., “Wavelet Approximation and Fourier Widths of Classes of Periodic Functions of Several Variables. II”, Anal. Math., 38:4 (2012), 249–289  crossref  isi
    24. A. O. Radomskii, “On nonequivalence of the $\mathrm{C}$- and $\mathrm{QC}$-norms in the space of trigonometric polynomials”, Sb. Math., 207:12 (2016), 1729–1742  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    25. Temlyakov V., “on the Entropy Numbers of the Mixed Smoothness Function Classes”, J. Approx. Theory, 217 (2017), 26–56  crossref  mathscinet  zmath  isi  scopus
    26. A. O. Radomskii, “On approximation characteristics of some classes of functions of small smoothness”, Siberian Math. J., 59:3 (2018), 486–493  mathnet  crossref  crossref  mathscinet  isi  elib
    27. F. Dai, A. Prymak, V. N. Temlyakov, S. Yu. Tikhonov, “Integral norm discretization and related problems”, Russian Math. Surveys, 74:4 (2019), 579–630  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    28. A. O. Radomskii, “Some trigonometric polynomials with extremely small uniform norm and their applications”, Izv. Math., 84:2 (2020), 361–391  mathnet  crossref  crossref  mathscinet  isi  elib
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