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Application of the Fourier transform to summability of fourier series

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Literature Cited

  1. A. Zygmund, Trigonometric Series, Cambridge Univ. Press (1968).

  2. G. E. Shilov, Mathematical Analysis, Vol. 2, MIT Press (1974).

  3. S. Bochner, Fourier Integrals [in German], Chelsea Publ.

  4. B. Nagy, “Sur une classe généralé de procédés de sommation pour les séries de Fourier,” Hungarica Acta Math.,1, No. 3, 14–52 (1948).

    Google Scholar 

  5. S. A. Telyakovskii, “Norms of trigonometric polynomials and approximation of differentiable functions by linear means of their Fourier series, I,” Tr. Mat. Inst., Akad. Nauk SSSR,62 (1961).

  6. H. Bateman and A. Erdelyi (editors), Higher Transcendental Functions, McGraw-Hill.

  7. R. O. Kuz'min, Bessel Functions [in Russian], State Technical and Theoretical Press (GTTI), Moscow-Leningrad (1933).

    Google Scholar 

  8. S. Bochner, “Summation of multiple Fourier series by spherical means,” Trans. Am. Math. Soc.,40, 175–207 (1936).

    Google Scholar 

  9. Ya. S. Bugrov, “Approximation by trigonometric polynomials of classes of functions defined by a polyharmonic operator,” Usp. Mat. Nauk,13, No. 2, 149–157 (1958).

    Google Scholar 

  10. N. Wiener, Fourier Integral and Certain of Its Applications, McGraw-Hill (1972).

  11. R. M. Trigub, “Linear methods of summation and absolute convergence of Fourier siries,” Izv. Akad. Nauk SSSR, Ser. Mat.,32, No. 1, 24–49 (1968).

    Google Scholar 

  12. R. M. Trigub, “Summability and absolute convergence of Fourier series in the large,” in: Metric Problems in the Theory of Functions and Mappings [in Russian], No. 2, Naukova Dumka, Kiev (1971), pp. 173–267.

    Google Scholar 

  13. A. G. Lebed', “Linear methods of summation and absolute convergence of double Fourier series,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 12, 91–102 (1971).

    Google Scholar 

  14. D. K. Faddeev, “On the representation of summable functions by singular integrals at Lebesgue points,” Mat. Sb.,1, 351–368 (1936).

    Google Scholar 

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 18, No. 3, pp. 497–511, May–June, 1977.

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Belinskii, É.S. Application of the Fourier transform to summability of fourier series. Sib Math J 18, 353–363 (1977). https://doi.org/10.1007/BF00967027

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  • DOI: https://doi.org/10.1007/BF00967027

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