Acta Mathematica

, Volume 81, Issue 1, pp 225–238 | Cite as

On the spectral synthesis of bounded functions

  • Arne Beurling


Bounded Function Weak Topology Positive Definite Function Spectral Synthesis Convergent Fourier Series 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    As is easily proved this definition leads to the same Λϕ as that obtained by the stronger topology used by the author in a previous paper;Un Théorème sur les fonctions bornées..., Acta math. vol. 77, 1945.Google Scholar
  2. 1.
    The result is to be published in C. R. de l'Academie des Sciences, vol. 227.Google Scholar
  3. 1.
    SeeBeurling:Sur une classe de fonctions presque-périodiques, C. R. de l'Acad. des Sciences, t. 225, pp. 326–7, 1947.MathSciNetGoogle Scholar
  4. 4.
    SeeBeurling:Sur les intégrales de Fourier absolument conrergentes..., C.R. du congrès des mathématiques à Helsingfors 1938.Google Scholar
  5. 5.
    For the general properties of these functions and their interesting connection with certain metrical problems in Hilbert space, see v.Neumann andSchoenberg:Fourier Integrals and Metric Geometry Transactions of the Amer. Math. Soc. V. 50, pp. 467–487, 1941.Google Scholar
  6. 6.
    Sur les spectres de fonctions, Conférence faite au Congrès sur l'Analyse harmonique à Nancy 1947, (unpublished but multigraphed).Google Scholar

Copyright information

© Almqvist & Wiksells Boktryckeri AB 1949

Authors and Affiliations

  • Arne Beurling
    • 1
  1. 1.Uppsala

Personalised recommendations