Skip to main content
SpringerLink
Log in

Extension of ultradifferentiable functions

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. C.A. Berenstein, B.A. Taylor, Interpolation problems in ℂn with applications to harmonic analysis, J. Anal. Math.38 (1980), 188–254

    MATH  MathSciNet  Google Scholar 

  2. A. Beurling, Quasianalyticity and general distributions, lectures 4 and 5, AMS Summer Institute, Stanford 1961

    Google Scholar 

  3. G. Björck, Linear partial differential operators and generalized distributions, Ark. Mat.6 (1966), 351–407

    MATH  MathSciNet  Google Scholar 

  4. J. Bonet, R. Meise, B.A. Taylor, Whitney's extension theorem for ultra-differentiable functions of Roumieu type, Proc. R. Ir. Acad.89A (1989), 53–66

    MathSciNet  Google Scholar 

  5. J. Bonet. R. Meise, B.A. Taylor, The range of the Borel map for classes of non-quasianalytic functions, preprint

  6. J. Bonet, R.W. Braun, R. Meise, B.A. Taylor, Whitney's extension theorem for non-quasianalytic classes of ultradifferentiable functions, preprint

  7. R.W. Braun, R. Meise, B.A. Taylor, Ultradifferentiable functions and Fourier analysis, Res. Math.17 (1990), 207–237

    MathSciNet  Google Scholar 

  8. M.D. Bronshtein, Continuation of functions in Carleman's non-quasi-analytical classes, Sov. Math. (Iz. VUZ)30, No. 12 (1986), 11–14

    MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  10. J. Bruna, On the punctual image of non-quasianalytic classes of functions, unpublished manuscript.

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

    MATH  MathSciNet  Google Scholar 

  12. G.A. Dzanasija, Carlemans problem for functions of the Gevrey class, Soviet Math. Dokl.3 (1962), 259–262

    MathSciNet  Google Scholar 

  13. L. Ehrenpreis, Fourier analysis in several complex variables, Van Nostrand 1967

  14. U. Franken, Stetige lineare Ausdehnungsoperatoren auf Räumen ultradifferenzierbarer Funktionen vom Beurling Typ, manuscript

  15. L. Hörmander, An introduction to complex analysis in several variables, North Holland/American Elsevier, New York 1973

    MATH  Google Scholar 

  16. L. Hörmander, The analysis of linear partial differential operators I+II, Grundlehren 256+257, Springer, Berlin/New York 1983

    Google Scholar 

  17. J.-M. Kantor, Classes non-quasi analytiques et decomposition des support des ultradistributions, An. Acad. brasil. Cienc.44 (1972), 171–180

    MathSciNet  Google Scholar 

  18. H. Komatsu, Ultradistributions I. Structure theorems and a characterization, J. Fac. Sci. Tokyo Ser. IA20 (1973), 25–105

    MATH  MathSciNet  Google Scholar 

  19. H. Komatsu, Ultradistributions II. The kernel theorem and ultradistributions with support in a submanifold, J. Fac. Sci. Tokyo Ser. IA24 (1977), 607–628

    MATH  MathSciNet  Google Scholar 

  20. M. Langenbruch, The splitting condition for the weighted σ-complex, to appear in Result. Math.

  21. M. Langenbruch, Extension of ultradifferentiable functions of Roumieu type, Arch. Math.51 (1988), 353–362

    Article  MATH  MathSciNet  Google Scholar 

  22. M. Langenbruch, Bases in spaces of ultradifferentiable functions with compact support, Math. Ann.281 (1988), 31–42

    Article  MATH  MathSciNet  Google Scholar 

  23. P. Lelong, L. Gruman Entire functions in several complex variables, Grundlehren 286, Springer, Berlin/New York 1986

    Google Scholar 

  24. R. Meise, B.A. Taylor, A decomposition lemma for entire functions and its application to spaces of ultradifferentiable functions, Math. Nachr.142, 45–72.

  25. R. Meise, B.A. Taylor, Linear extension operators for ultradifferentiable functions of Beurling type on compact sets, Amer. J. Math.111 (1989), 309–337

    Article  MATH  MathSciNet  Google Scholar 

  26. R. Meise, B.A. Taylor, Whitney's extension theorem for ultradifferentiable functions of Beurling type, Ark. Mat.26 (1988), 265–287

    Article  MATH  MathSciNet  Google Scholar 

  27. B.S. Mityagin, An infinitely differentiable function with the value of its derivatives given at a point, So. Math. Dokl.2 (1961), 594–597

    MATH  Google Scholar 

  28. M. Neymark, On the Laplace transform of functionals on classes of infinitely differentiable functions, Ark. Math.7 (1968), 577–594

    MathSciNet  Google Scholar 

  29. A. Papaspyrou, oral communication 1991

  30. H.J. Petzsche, On E. Borel's theorem, Math. Ann.282 (1988), 299–313

    Article  MATH  MathSciNet  Google Scholar 

  31. de Roever, Extensions of ultradifferentiable functions on closed sets, in “Generalized functions and their applications in mathematical physics”, Proc. Int. Conf. Moscow 1980 (1981), 442–455

  32. C. Roumieu, Sur quelques extensions de la notion de distributions, Ann. Sci. Ecole Norm. Sup. Paris, 3 Ser.77 (1960), 41–121

    MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  34. G. Wahde, Interpolation in non-quasi-analytic classes of infinitely differentiable functions, Math. Scand.20 (1967), 17–35

    Google Scholar 

  35. H. Whitney, Analytic extensions of differentiable functions defined on closed sets, Trans. Amer. Math. Soc.36 (1934), 63–89

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FB 7-Mathematik, Universität-GHS Wuppertal, Gaußstr. 20, D-42097, Wuppertal 1, Germany

    Michael Langenbruch

Authors
  1. Michael Langenbruch
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Langenbruch, M. Extension of ultradifferentiable functions. Manuscripta Math 83, 123–143 (1994). https://doi.org/10.1007/BF02567604

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567604

Keywords

Search

Navigation