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On the best approximations of functions defined on zero-dimensional groups

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Ukrainian Mathematical Journal Aims and scope

We present a survey of results obtained by the author, his disciples, and other mathematicians and related to the problem of finding the best approximations of functions in the investigation of properties of spaces of functions defined on zero-dimensional compact commutative groups.

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References

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

    Google Scholar 

  2. M. F. Timan and A. I. Rubinshtein, “On the imbeddings of the classes of functions defined on zero-dimensional groups,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 8 (1980).

  3. M. F. Timan, “Best approximation of functions and linear methods for the summation of Fourier series,” Izv. Akad. Nauk SSSR, Ser. Mat., 29, No. 3, 587–604 (1965).

    MathSciNet  MATH  Google Scholar 

  4. N. Ya. Vilenkin, Theory of Multiplicative Systems. An Addition to the Book by S. Kaczmarz and H. Steinhaus, “Theorie der Orthogonalreihen” [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

  5. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities [Russian translation], Inostrannaya Literatura, Moscow (1948).

    Google Scholar 

  6. G. Morgenthaler, “Walsh–Fourier series,” Trans. Amer. Math. Soc. 84, No. 2, 472–507 (1947).

    Article  MathSciNet  Google Scholar 

  7. S. B. Stechkin, “On the absolute convergence of Fourier series,” Izv. Akad. Nauk SSSR, Ser. Mat., 17, No. 2, 87–98 (1953).

    MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  9. B. I. Golubev, “On one class of complete orthogonal systems,” Sib. Mat. Zh., 9, No. 2, 597–310 (1968).

    MathSciNet  Google Scholar 

  10. S. L. Blyumin, “On linear methods for the summation of Fourier series over multiplicative systems,” Sib. Mat. Zh., 9, No. 2, 449–455 (1968).

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  12. M. F. Timan, Approximation and Properties of Periodic Functions [in Russian], Naukova Dumka, Kiev (2009).

    Google Scholar 

  13. M. F. Timan and K. Tukhliev, Properties of Some Orthonormal Systems [in Russian], Deposited at VINITI No. 4929-80, Dnepropetrovsk (1980).

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Authors and Affiliations

  1. Dnepropetrovsk Agrarian University, Dnepropetrovsk, Ukraine

    M. F. Timan

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  1. M. F. Timan
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 5, pp. 719–728, May, 2012.

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Timan, M.F. On the best approximations of functions defined on zero-dimensional groups. Ukr Math J 64, 823–834 (2012). https://doi.org/10.1007/s11253-012-0681-6

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  • DOI: https://doi.org/10.1007/s11253-012-0681-6

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