Arkiv för Matematik

, Volume 26, Issue 1–2, pp 265–287

Whitney’s extension theorem for ultradifferentiable functions of Beurling type

  • Reinhold Meise
  • B. Alan Taylor


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baernstein II, A., Representation of holomorphic functions by boundary integrals,Trans. Amer. Math. Soc. 160 (1971), 27–37.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Beurling, A.,Quasi-analyticity and general distributions, Lectures 4 and 5, AMS Summer Institute, Stanford, 1961.Google Scholar
  3. 3.
    Björck, G., Linear partial differential operators and generalized distributions,Ark. Mat. 6 (1965), 351–407.CrossRefGoogle Scholar
  4. 4.
    Boas, R. P.,Entire functions, Academic Press, 1954.Google Scholar
  5. 5.
    Borel, E., Sur quelques points de la théorie des fonctions,Ann. École Norm. Sup. (3)12 (1895), 9–55.MathSciNetGoogle Scholar
  6. 6.
    Braun, R. W., Meise, R. andTaylor, B. A., Ultradifferentiable functions and Fourier analysis, manuscript.Google Scholar
  7. 7.
    Bronshtein, M. D., Continuation of functions in Carleman’s non-quasianalytical classes, Soviet Math. (Iz. VUZ)30, No. 12 (1986), 11–14.MathSciNetGoogle Scholar
  8. 8.
    Bruna, J., An extension theorem of Whitney type for non-quasianalytic classes of functions,J. London Math. Soc. (2),22 (1980), 495–505.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Carleson, L., On universal moment problems,Math. Scand. 9 (1961), 197–206.MATHMathSciNetGoogle Scholar
  10. 10.
    Dzanasija, G. A., Carleman’s problem for functions of the Gevrey class,Soviet Math. Dokl. 3 (1962), 969–972, translated fromDokl. Akad. Nauk SSSR 145 (1962), 259–262.Google Scholar
  11. 11.
    Ehrenpreis, L.,Fourier analysis in several complex variables, Wiley-Interscience Publ. 1970.Google Scholar
  12. 12.
    Hörmander, L.,An introduction, to complex analysis in several variables, Van Nostrand, 1967.Google Scholar
  13. 13.
    Hörmander, L.,Linear partial differential operators, Springer Verlag, 1969.Google Scholar
  14. 14.
    Komatsu, H., Ultradistributions I, Structure theorems and a characterization,J. Fac. Sci. Tokyo, Sect IA Math. 20 (1973), 25–105.MATHMathSciNetGoogle Scholar
  15. 15.
    Komatsu, H., Ultradistributions II, The kernel theorem and ultradistributions with support in a submanifold,J. Fac. Sci. Tokyo. Sect. IA Math. 24 (1977), 607–628.MATHMathSciNetGoogle Scholar
  16. 16.
    Malgrange, B.,Ideals of differentiable functions, Oxford University Press, 1966.Google Scholar
  17. 17.
    Meise, R., Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals,J. reine angew. Math. 363 (1985), 59–95.MATHMathSciNetGoogle Scholar
  18. 18.
    Meise, R. andTaylor, B. A., Sequence space representations for (FN)-algebras of entire functions modulo closed ideals,Studia Math. 85 (1987), 203–227.MATHMathSciNetGoogle Scholar
  19. 19.
    Meise, R. andTaylor, B. A., Splitting of closed ideals in (DFN)-algebras of entire functions and the property (DN),Trans. Amer. Math. Soc. 302 (1987), 321–370.CrossRefMathSciNetGoogle Scholar
  20. 20.
    Meise, R. andTaylor, B. A., Opérateurs linéaires continus d’extension pour les fonctions ultradifférentiables sur des intervalles compacts,C.R. Acad. Sci. Paris Sér. I Math. 302 (1986), 219–222.MATHMathSciNetGoogle Scholar
  21. 21.
    Meise, R. andTaylor, B. A., Linear extension operators for ultradifferentiable functions on compact sets, to appear inAmer. J. Math. (1988).Google Scholar
  22. 22.
    Mityagin, B. S., An indefinitely differentiable function with the values of its derivatives given at a point,Soviet Math. Dokl. 2 (1961), 594–597, translated fromDokl. Akad. Nauk SSSR 138 (1961), 289–292.MATHGoogle Scholar
  23. 23.
    Mityagin, B. S., Approximate dimension and bases in nuclear spaces,Russian Math. Surveys 16 (1961), 59–127, translated fromUspekhi Mat. Nauk 16 (1961), 63–132.MATHCrossRefGoogle Scholar
  24. 24.
    Petzsche, H.-J., On E. Borel’s theorem, preprint, (1987).Google Scholar
  25. 25.
    Schaefer, H. H.,Topological vector spaces, Springer, 1971.Google Scholar
  26. 26.
    Taylor, B. A., Analytically uniform spaces of infinitely differentiable functions.Comm. Pure. Appl. Math. 24 (1971), 39–51.MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Tidten, M., Fortsetzung vonC -Funktionen, welche auf einer abgeschlossenen, Menge inR n definiert sind,Manuscripta Math. 27 (1979), 291–312.MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Vogt, D., Charakterisierung der Unterräume vons, Math. Z. 155 (1977), 109–117.MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Vogt, D., Sequence space representations of spaces of test functions and distributions, pp. 405–433,Functional analysis, holomorphy and approximation theory, G. Zapata (Ed.), Marcel Dekker, Lect. Notes in Pure and Appl. Math.83 (1983).Google Scholar
  30. 30.
    Wahde, G., Interpolation in non-quasi-analytic classes of infinitely differentiable function,Math. Scand. 20 (1967), 19–31.MATHMathSciNetGoogle Scholar

Copyright information

© Institut Mittag-Leffler 1988

Authors and Affiliations

  • Reinhold Meise
    • 1
  • B. Alan Taylor
    • 2
  1. 1.Mathematisches Institut der Universität DüsseldorfDüsseldorfFed. Rep. of Germany
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

Personalised recommendations