Advertisement

New Integrals pp 180-200 | Cite as

Analysis of P. Malliavin's proof of non spectral synthesis

  • J. D. Stegeman
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1419)

Keywords

Finite Order Compact Abelian Group Closed Ideal Technical Construction Tauberian Theorem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J.J. Benedetto-Spectral synthesis. Stuttgart: B.G. Teubner 1975.CrossRefzbMATHGoogle Scholar
  2. [2]
    A. Beurling-Sur les intégrales de Fourier absolument convergentes et leur application à une transformation fonctionnelle. IXe Congrès des Math. Scand., Helsinki, August 1938, 345–366 (1938).Google Scholar
  3. [3]
    C.C. Graham, O.C. McGehee-Essays in commutative harmonic analysis. New York, etc.: Springer-Verlag 1979.CrossRefzbMATHGoogle Scholar
  4. [4]
    H. Helson-On the ideal structure of group algebras. Ark.Mat. 2, 83–86 (1952).MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    C.S. Herz-The spectral theory of bounded functions. Transactions Amer. Math. Soc. 94, 181–232 (1960).MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    E. Hewitt, K.A. Ross-Abstract harmonic analysis, Vol. II. Berlin etc.: Springer-Verlag 1970.zbMATHGoogle Scholar
  7. [7]
    J.-P. Kahane, R. Salem-Ensembles parfaits et séries trigonométriques. Paris: Hermann 1963.zbMATHGoogle Scholar
  8. [8]
    P. Malliavin-Impossibilité de la synthèse spectrale sur les groupes abéliens non compacts. Inst. Hautes Etudes Sci. Publ. Math. 2, 61–68 (1959).MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    H. Reiter-Classical harmonic analysis and locally compact groups. Oxford: At the Clarendon Press 1968.zbMATHGoogle Scholar
  10. [10]
    I. Richards-On the disproof of spectral synthesis. J. Comb. Theory 2, 61–70 (1967).MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    W. Rudin-Fourier analysis on groups. Interscience Tract No. 12. New York: Wiley 1962.zbMATHGoogle Scholar
  12. [12]
    L. Schwartz-Sur une propriété de synthèse spectrale dans les groupes non compacts. C.R. Acad. Sci. Paris 227, 424–426 (1948).MathSciNetzbMATHGoogle Scholar
  13. [13]
    J.D. Stegeman-Extension of a theorem of H. Helson. Int. Congress Math., Moscow, Abstracts, Section 5, p.28 (1966).Google Scholar
  14. [14]
    J.D. Stegeman-Studies in Fourier and tensor algebras. Thesis. Utrecht: Pressa Trajectina 1971.Google Scholar
  15. [15]
    J.D. Stegeman-On Malliavin's proof of non spectral synthesis. Real Analysis Exchange 14 (1), 30–33 (1988–1989).Google Scholar
  16. [16]
    N. Wiener-Tauberian theorems. Annals of Math. 33, 1–100 (1932).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • J. D. Stegeman
    • 1
  1. 1.Department of MathematicsUniversity of UtrechtUtrechtThe Netherlands

Personalised recommendations