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Ukrainian Mathematical Journal

, Volume 65, Issue 12, pp 1904–1911 | Cite as

On the Absolute Summability of Fourier Series of Almost Periodic Functions

  • Yu. Kh. Khasanov
Article
  • 70 Downloads

We establish new sufficient conditions for the absolute |C, α|-summability of the Fourier series of functions almost periodic in a sense of Besicovitch whose spectrum has limit points at infinity and at the origin for \( \alpha \ge \frac{1}{2} \).

Keywords

Fourier Series Periodic Function English Translation Limit Point Trigonometric Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    K. Tandori, “Über die orthogonalen Funktionen IX (Absolute Summation),” Acta Sci. Math., 21, 292–299 (1960).zbMATHMathSciNetGoogle Scholar
  2. 2.
    L. Leindler, “Über die absolute Summierbarkeit der Orthogonalreihen,” Acta Sci. Math., 22, 243–268 (1961).zbMATHMathSciNetGoogle Scholar
  3. 3.
    P. Billard, “Sur la sommabilitie absolute des series de fonctions orthogonales,” Bull. Sci. Math., 85, 29–31 (1961).zbMATHMathSciNetGoogle Scholar
  4. 4.
    L. V. Grepachevskaya, “Absolute summability of orthogonal series,” Mat. Sb., 65 (107), No. 3, 370–389 (1964).Google Scholar
  5. 5.
    L. V. Grepachevskaya, “On the absolute summability by the Cesàro, Riesz, and Zygmund methods,” Dokl. Akad. Nauk SSSR, 155, No. 3, 370–389 (1964).Google Scholar
  6. 6.
    M. F. Timan, “On the absolute convergence and summability of Fourier series,” Soobshch. Akad. Nauk Gruz. SSSR, 26, No. 6, 641–646 (1961).zbMATHMathSciNetGoogle Scholar
  7. 7.
    M. F. Timan and Yu. Kh. Khasanov, “On the absolute summability of Fourier series of almost-periodic Besicovitch functions,” Ukr. Mat. Zh., 61, No. 9, 1267–1276 (2009); English translation : Ukr. Math. J., 61, No. 9, 1499–1510 (2009).CrossRefMathSciNetGoogle Scholar
  8. 8.
    A. S. Besicovitch, Almost Periodic Functions, Cambridge University Press, Cambridge (1932).Google Scholar
  9. 9.
    B. M. Levitan, Almost Periodic Functions [in Russian], Gostekhteorizdat, Moscow (1953).Google Scholar
  10. 10.
    G. Sunouchi, “On the absolute summability of Fourier series,” J. Math. Soc. Jap., 1, No. 2, 57–65 (1949).CrossRefzbMATHGoogle Scholar
  11. 11.
    G. H. Hardy, J. E. Littlewood, and G. P’olya, Inequalities [Russian translation], Inostrannaya Literatura, Moscow (1948).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yu. Kh. Khasanov
    • 1
  1. 1.Russian–Tajik Slavic UniversityDushanbeTajikistan

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