Fourier Transforms (I)

  • Toru Maruyama
Part of the Monographs in Mathematical Economics book series (MOME, volume 2)


The objects of classical theory of Fourier series discussed in the preceding chapter are periodic functions. Is it possible to construct an analogous theory for nonperiodic functions? It is the theory of Fourier transforms which answers this question positively.


  1. 1.
    Cartan, H.: Théorie élémentaires des fonctions analytiques d’une ou plusieurs variables complexes. Hermann, Paris (1961) (English edn.) Elementary Theory of Analytic Functions of One or Several Complex Variables. Addison Wesley, Reading (1963) Google Scholar
  2. 2.
    Dym, H., McKean, H.P.: Fourier Series and Integrals. Academic Press, New York (1972) Google Scholar
  3. 3.
    Goldberg, R.R.: Fourier Transforms. Cambridge University Press, Cambridge (1961) Google Scholar
  4. 4.
    Kawata, T.: Fourier Henkan to Laplace Henkan (Fourier Transforms and Laplace Transforms). Iwanami Shoten, Tokyo (1957) (Originally published in Japanese) Google Scholar
  5. 5.
    Kawata, T.: Fourier Kaiseki (Fourier Analysis). Sangyo Tosho, Tokyo (1975) (Originally published in Japanese) Google Scholar
  6. 6.
    Kolmogorov, A.N., Fomin, S.V.: (English edn.) Introductory Real analysis. Prentice-Hall, New York (1970) (Japanese edn. translated from 4th edn.) Kansu-kaiseki no Kiso, 4th edn. Iwanami Shoten, Tokyo (1979) (Originally published in Russian). I use the Japanese edition for quotations. Google Scholar
  7. 7.
    Schwartz, L.: Méthods mathématique pour les sciences physiques. Hermann, Paris (1965) Google Scholar
  8. 8.
    Stromberg, K.R.: An Introduction to Classical Real Analysis. American Mathematical Society, Providence (1981) Google Scholar
  9. 9.
    Takagi, T.: Kaiseki Gairon (Treatise on Analysis), 3rd edn. Iwanami Shoten, Tokyo (1961) (Originally published in Japanese) Google Scholar
  10. 10.
    Titchmarsh, E.C.: Introduction to the Theory of Fourier Integrals, 2nd edn. Oxford, London (1948) Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Toru Maruyama
    • 1
  1. 1.Professor EmeritusKeio UniversityTokyoJapan

Personalised recommendations