Advertisement

Israel Journal of Mathematics

, Volume 54, Issue 1, pp 60–70 | Cite as

Convolution equations and spaces of ultradifferentiable functions

  • Daniele C. Struppa
Article
  • 37 Downloads

Abstract

We study spaces of “approximate solutions” to a given convolution equation. In particular we show how their quasianalyticity can be reduced to the study of a suitably constructed Cauchy problem for related spaces. We give a unicity theorem for this problem.

Keywords

Cauchy Problem Entire Function Differentiable Function Uniform Space Partial Differential Operator 
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.
    C. A. Berenstein and M. A. Dostal,Analytically Uniform Spaces and their Applications to Convolution Equations, Lecture Notes in Math., no. 256, springer-Verlag, Berlin, 1972.Google Scholar
  2. 2.
    C. A. Berenstein and J. Lesmes,The Cauchy problem for convolution operators. Uniqueness, Michigan Math. J.26 (1979), 333–349.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    C. A. Berenstein and B. A. Taylor,Interpolation problems in C n with applications to harmonic analysis, J. Analyse Math.38 (1980), 188–254.MATHMathSciNetGoogle Scholar
  4. 4.
    G. Björck,Linear partial differential operators and generalized distributions, Ark. Mat.6 (1966), 351–407.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    L. Ehrenpreis,Fourier Analysis in Several Complex Variables, Wiley-Interscience, New York, 1970.MATHGoogle Scholar
  6. 6.
    S. Hansen,Uniqueness of the Cauchy problem for convolution equations, J. Reine Angew. Math.317 (1980), 1–15.MATHMathSciNetGoogle Scholar
  7. 7.
    L. Hörmander,La transformation de Legendre et la théorème de Paley-Wiener, C. R. Seances Acad. Sci.240 (1955), 392–395.MATHGoogle Scholar
  8. 8.
    R. E. A. C. Paley and N. Wiener,Fourier Transforms in the Complex Domain, Amer. Math. Soc., New York, 1934.MATHGoogle Scholar
  9. 9.
    C. Roumieu,Sur quelques extensions de la notion de distribution, Ann. Sci. Ecole Norm. Sup. 3 ser.,77 (1960), 41–121.MATHMathSciNetGoogle Scholar
  10. 10.
    B. A. Taylor,A semi-norm topology for some (DF)-spaces of entire functions, Duke Math. J.38 (1971), 379–385.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    S. Täcklind,Sur les classes quasianalytiques des solutions des équations aux dérivées partielles du type parabolique, Nova Acta R. Soc. Sci. Ups.10 (1936), 1–56.Google Scholar

Copyright information

© Hebrew University 1986

Authors and Affiliations

  • Daniele C. Struppa
    • 1
  1. 1.Scuola Normale Superiore, Piazza dei CavalieriPisaItaly

Personalised recommendations