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On the best L 2-approximations of functions by using wavelets

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Ukrainian Mathematical Journal Aims and scope

We deduce the exact Jackson-type inequalities for the approximations of functions ƒ ∈ L 2(ℝ) in L 2(ℝ) by using partial sums of wavelet series in the cases of Meyer and Shannon-Kotelnikov wavelets.

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References

  1. N. P. Korneichuk, “On the exact constant in the Jackson inequality for continuous periodic functions, ” Dokl. Akad. Nauk SSSR, 145, No. 3, 514–515 (1962).

    MathSciNet  Google Scholar 

  2. N. I. Chernykh, “On the Jackson inequality in L 2,” Tr. Mat. Inst. Akad. Nauk SSSR, 88, 71–74 (1967).

    Google Scholar 

  3. N. I. Chernykh, “On the best approximation of periodic functions by trigonometric polynomials in L 2,” Mat. Zametki, 2, No. 5, 513–522 (1967).

    MathSciNet  Google Scholar 

  4. I. I. Ibragimov and F. G. Nasibov, “Estimation of the best approximation of a summable function on the real axis by entire functions of finite powers,” Dokl. Akad. Nauk SSSR, 194, No. 5, 1113–1116 (1970).

    MathSciNet  Google Scholar 

  5. V. Yu. Popov, “On the best mean-square approximations by entire functions of the exponential type, ” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 6, 65–73 (1972).

  6. A. A. Ligun, “Exact Jackson-type inequalities for periodic functions in the space L 2,” Mat. Zametki, 43, No. 6, 757–769 (1988).

    MathSciNet  Google Scholar 

  7. V. A. Yudin, “Diophantine approximations in extremal problems,” Dokl. Akad. Nauk SSSR, 251, No. 1, 54–57 (1980).

    MathSciNet  Google Scholar 

  8. A. G. Babenko, “On the exact constant in the Jackson inequality in L 2,” Mat. Zametki, 39, No. 5, 651–664 (1986).

    MathSciNet  Google Scholar 

  9. V. V. Arestov and N. I. Chernykh, “On the L 2-approximation of periodic functions by trigonometric polynomials,” in: Proc. of the Internat. Conf. “Approximation and Funct. Spaces” (Gdansk, 1979), North-Holland, Amsterdam (1981), pp. 5–43.

    Google Scholar 

  10. V. V. Volchkov, “On the exact constants in the Jackson inequality in the space L 2,” Ukr. Mat. Zh., 47, No. 1, 108–110 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  11. S. B. Vakarchuk, “On the best polynomial approximations of 2π-periodic functions and exact values of n-widths of functional classes in the space L 2,” Ukr. Mat. Zh., 54, No. 12, 1603–1615 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  12. B. S. Kashin and A. A. Saakyan, Orthogonal Series [in Russian], AFTs, Moscow (1999).

    Google Scholar 

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Authors and Affiliations

  1. Dnepropetrovsk National University, Dnepropetrovsk, Ukraine

    V. F. Babenko & G. S. Zhiganova

  2. Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, Donetsk, Ukraine

    V. F. Babenko

Authors
  1. V. F. Babenko
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  2. G. S. Zhiganova
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 8, pp. 1119–1127, August, 2008.

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Babenko, V.F., Zhiganova, G.S. On the best L 2-approximations of functions by using wavelets. Ukr Math J 60, 1307–1317 (2008). https://doi.org/10.1007/s11253-009-0124-1

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  • DOI: https://doi.org/10.1007/s11253-009-0124-1

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