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Approximation in Lp by means of piecewise-constant functions

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Literature cited

  1. G. N. Agaev, N. Ya. Vilenkin, G. M. Dzhafarli, and A. I. Rubinshtein, Multiplicative Systems of Functions and Harmonic Analysis of Groups of Zero Measure [in Russian], Elm, Baku (1981).

    Google Scholar 

  2. N. Ya. Vilenkin, “On a class of complete orthonormalized systems,” Izv. Akad. Nauk SSSR, Ser. Mat.,11, 363–400 (1947).

    Google Scholar 

  3. C. Watari, “Best approximation by Walsh polynomials,” Tohoku math. J.,15, No. 1, 1–5 (1963).

    Google Scholar 

  4. A. V. Efimov, “On some approximate properties of periodic multiplicative orthonormalized systems,” Mat. Sb.,69, No. 3, 354–370 (1966).

    Google Scholar 

  5. N. Ya. Vilenkin and A. I. Rubinshtein, “A theorem of S. B. Stechkin on absolute convergence and series with respect to systems of characters of zero-measure Abelian groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 3–9 (1975).

    Google Scholar 

  6. L. R. Williams and J. H. Wells, “Lp-inequalities,” J. Math. Anal. Appl.,64, No. 3, 518–529 (1978).

    Google Scholar 

  7. A. Benedeck and R. Panzone, “The spaces Lp with mixed norm,” Duke Math. J.,28, 301–324 (1961).

    Google Scholar 

  8. V. I. Berdyshev, “On a theorem of Jackson in Lp,” Tr. Mat. Inst., Akad. Nauk SSSR,88, 3–16 (1967).

    Google Scholar 

  9. I. M. Vinogradov, Foundations of Number Theory [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  10. J. Brillhart and P. Morton, “Über summen von Rudin-Shapiroschen koeffizienten,” Illinois J. Math.,22, 126–148 (1978).

    Google Scholar 

  11. A. Yu. Olevskii, “On the extension of a sequence of functions to a complete orthonormalized system,” Mat. Zametki,6, No. 6, 737–747 (1969).

    Google Scholar 

  12. V. V. Petrov, Sums of Independent Random Variables, Academic Press (1960).

  13. B. S. Kashin, “On Weyl's multipliers for almost everywhere convergence of orthogonal series,” Anal. Math.,2, No. 4, 249–266 (1976).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 44, No. 1, pp. 64–79, July, 1988.

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Ivanov, V.I. Approximation in Lp by means of piecewise-constant functions. Mathematical Notes of the Academy of Sciences of the USSR 44, 523–532 (1988). https://doi.org/10.1007/BF01158118

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  • DOI: https://doi.org/10.1007/BF01158118

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