Pointwise Convergence of Fourier Series

  • Pierre Brémaud


The inversion formula for Fourier series obtained in Chapter A2 requires a rather strong condition of summability of the Fourier coefficients series. Moreover, this condition implies that the function itself is almost everywhere equal to a continuous function. In this section, the class of functions for which the inversion formula holds is extended.


Fourier Series Fourier Coefficient Inversion Formula Pointwise Convergence Poisson Formula 
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  1. [A1]
    Ablowitz, M.J. and Jokas, A.S. (1997). Complex Variables, Cambridge University Press.zbMATHGoogle Scholar
  2. [A2]
    Bracewell, R.N. (1991). The Fourier Transform and Its Applications, 2nd rev. ed., McGraw-Hill; New York.Google Scholar
  3. [A3]
    Gasquet, C. and Witomski, P. (1991). Analyse de Fourier et Applications, Masson: Paris.Google Scholar
  4. [A4]
    Helson, H. (1983). Harmonic Analysis, Addison-Wesley: Reading, MA.zbMATHGoogle Scholar
  5. [A5]
    Katznelson, Y. (1976). An Introduction to Harmonic Analysis, Dover: New York.zbMATHGoogle Scholar
  6. [A6]
    Kodaira, K. (1984). Introduction to Complex Analysis, Cambridge University Press.zbMATHGoogle Scholar
  7. [A7]
    Körner, T.W. (1988). Fourier Analysis, Cambridge University Press.zbMATHGoogle Scholar
  8. [A8]
    Rudin, W. (1966). Real and Complex Analysis, McGraw-Hill: New York.zbMATHGoogle Scholar
  9. [A9]
    Titchmarsh, E.C. (1986). The Theory of Functions, Oxford University Press.Google Scholar
  10. [A10]
    Tolstov, G. (1962). Fourier Series, Prentice-Hall (Dover edition, 1976).Google Scholar
  11. [A11]
    Zygmund, A. (1959). Trigonometric Series, (2nd ed., Cambridge University Press.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Pierre Brémaud
    • 1
    • 2
  1. 1.École Polytechnique Fédérale de LausanneSwitzerland
  2. 2.INRIA/École Normale SupérieureFrance

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