Skip to main content
Log in

Whitney’s extension theorem for ultradifferentiable functions of Beurling type

  • Published:
Arkiv för Matematik

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Baernstein II, A., Representation of holomorphic functions by boundary integrals,Trans. Amer. Math. Soc. 160 (1971), 27–37.

    Article  MATH  MathSciNet  Google Scholar 

  2. Beurling, A.,Quasi-analyticity and general distributions, Lectures 4 and 5, AMS Summer Institute, Stanford, 1961.

    Google Scholar 

  3. Björck, G., Linear partial differential operators and generalized distributions,Ark. Mat. 6 (1965), 351–407.

    Article  Google Scholar 

  4. Boas, R. P.,Entire functions, Academic Press, 1954.

  5. Borel, E., Sur quelques points de la théorie des fonctions,Ann. École Norm. Sup. (3)12 (1895), 9–55.

    MathSciNet  Google Scholar 

  6. Braun, R. W., Meise, R. andTaylor, B. A., Ultradifferentiable functions and Fourier analysis, manuscript.

  7. Bronshtein, M. D., Continuation of functions in Carleman’s non-quasianalytical classes, Soviet Math. (Iz. VUZ)30, No. 12 (1986), 11–14.

    MathSciNet  Google Scholar 

  8. Bruna, J., An extension theorem of Whitney type for non-quasianalytic classes of functions,J. London Math. Soc. (2),22 (1980), 495–505.

    Article  MATH  MathSciNet  Google Scholar 

  9. Carleson, L., On universal moment problems,Math. Scand. 9 (1961), 197–206.

    MATH  MathSciNet  Google Scholar 

  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. Ehrenpreis, L.,Fourier analysis in several complex variables, Wiley-Interscience Publ. 1970.

  12. Hörmander, L.,An introduction, to complex analysis in several variables, Van Nostrand, 1967.

  13. Hörmander, L.,Linear partial differential operators, Springer Verlag, 1969.

  14. Komatsu, H., Ultradistributions I, Structure theorems and a characterization,J. Fac. Sci. Tokyo, Sect IA Math. 20 (1973), 25–105.

    MATH  MathSciNet  Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

  16. Malgrange, B.,Ideals of differentiable functions, Oxford University Press, 1966.

  17. Meise, R., Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals,J. reine angew. Math. 363 (1985), 59–95.

    MATH  MathSciNet  Google Scholar 

  18. Meise, R. andTaylor, B. A., Sequence space representations for (FN)-algebras of entire functions modulo closed ideals,Studia Math. 85 (1987), 203–227.

    MATH  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

  21. Meise, R. andTaylor, B. A., Linear extension operators for ultradifferentiable functions on compact sets, to appear inAmer. J. Math. (1988).

  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.

    MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  24. Petzsche, H.-J., On E. Borel’s theorem, preprint, (1987).

  25. Schaefer, H. H.,Topological vector spaces, Springer, 1971.

  26. Taylor, B. A., Analytically uniform spaces of infinitely differentiable functions.Comm. Pure. Appl. Math. 24 (1971), 39–51.

    Article  MATH  MathSciNet  Google Scholar 

  27. Tidten, M., Fortsetzung vonC -Funktionen, welche auf einer abgeschlossenen, Menge inR n definiert sind,Manuscripta Math. 27 (1979), 291–312.

    Article  MATH  MathSciNet  Google Scholar 

  28. Vogt, D., Charakterisierung der Unterräume vons, Math. Z. 155 (1977), 109–117.

    Article  MATH  MathSciNet  Google Scholar 

  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).

  30. Wahde, G., Interpolation in non-quasi-analytic classes of infinitely differentiable function,Math. Scand. 20 (1967), 19–31.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meise, R., Taylor, B.A. Whitney’s extension theorem for ultradifferentiable functions of Beurling type. Ark. Mat. 26, 265–287 (1988). https://doi.org/10.1007/BF02386123

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02386123

Keywords

Navigation