Some Results on the Absolutely Convergent Series of Functions and of Distributions

  • Nicolas K. Artemiadis
Part of the NATO ASI Series book series (ASIC, volume 315)

Abstract

Let A be the class of all Lebesgue integrable complex-valued functions on the circle T (the additive group of the reals modulo 2π) with absolutely convergent Fourier series and let A be the collection of all continuous functions in A

Keywords

Fourier Series Fourier Coefficient Trigonometric Polynomial Convergent Series Translation Operator 
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References

  1. [1]
    N. Artemiadis, “Criteria for absolute convergence of Fourier Series” Proc. Amer. Math. Soc. 50 (1975), 179–183.MathSciNetMATHGoogle Scholar
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    N. Artemiadis, “Quelques résultats sur les transformées de Fourier avec applications” Bull. Sc. Math., 2e serie, 97, 1973, 177–191. MathSciNetGoogle Scholar
  3. [3]
    N. Artemiadis, “Absolutely convergent Fourier series of distributions” Proc. Amer. Math. Soc. 83 (1981), 276–278.MathSciNetMATHGoogle Scholar
  4. [4]
    R.E. Edwards, “Fourier Series” vols. I, II, Holt, Rinehart and Winston, New York, 1967. Google Scholar
  5. [5]
    J.-P. Kahane, “Séries de Fourier absolument convergentes” Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin and New York, 1970, MR 43 # 801. Google Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Nicolas K. Artemiadis
    • 1
  1. 1.ThrakomakedonesGreece

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