Skip to main content
SpringerLink
Log in

On E. Borel's theorem

  • Published:
Mathematische Annalen 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. Borel, E.: Sur quelques points de la théorie des fonctions. Ann. Sci. Éc. Norm. Super, IV. Set.12, 9–55 (1985)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  4. Dzanasija, G.A.: Carleman's problem for functions of the Gevrey class. Sov. Math., Dokl.3, 969–972 (1962) [translated from Dokl. Akad. Nauk. SSSR145, 259–262 (1962)]

    Google Scholar 

  5. Ehrenpreis, L.: Fourier analysis in several complex variables. New York: Wiley 1970

    Google Scholar 

  6. Grothendieck, A.: Produits tensoriels topologiques et espaces nucléaires. Providence, R.I.: Am. Math. Soc. 1973

    Google Scholar 

  7. Hörmander, L.: The analysis of linear partial differential operators. I. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  8. Komatsu, H.: Ultradistributions. II. The Kernel theorem and ultradistributions with support in a submanifold. J. Fac. Sci., Univ. Tokyo, Sect. I A24, 607–628 (1977)

    Google Scholar 

  9. Langenbruch, M.: Ultradifferentiable functions on compact intervals. Preprint

  10. Langenbruch, M.: Bases in spaces of ultradifferentiable functions with compact support. Preprint

  11. Meise, R., Taylor, B.A.: Opérateurs linéaires continus d'extension pour les fonctions ultradifferentiables sur des intervalls compacts. C.R. Acad. Sci. Paris302, 219–222 (1986)

    Google Scholar 

  12. Meise, R., Taylor, B.A.: Linear extension operators for ultradifferentiable functions on compact sets. Preprint

  13. Meise, R., Taylor, B.A.: Whitney's extension theorem for ultradifferentiable functions of Beurling type. Preprint

  14. Mityagin, B.S.: An indefinitely differentiable function with the values of its derivatives given at a point. Sov. Math., Dokl.2, 594–597 (1961) [translated from Dokl. Akad. Nauk SSSR138, 289–292 (1961)]

    Google Scholar 

  15. Mityagin, B.S.: Approximate dimension and bases in nuclear spaces. Russ. Math. Surv.16, 59–127 (1961) [translated from Usp. Math. Nauk16, 63–132 (1961)]

    Google Scholar 

  16. Petzsche, H.-J.: Some results of Mittag-Leffler-type for vector valued functions and spaces of class 313-1. In: Bierstedt, K.-D., Fuchssteiner, B. (eds.). Functional analysis: surveys and recent results. II. Amsterdam. North-Holland 1980

    Google Scholar 

  17. Petzsche, H.-J., Vogt, D.: Almost analytic extension of ultradifferentiable functions and the boundary values of holomorphic functions. Math. Ann.267, 17–35 (1984)

    Google Scholar 

  18. Vogt, D.: Subspaces and quotient spaces of (s). In: Biertedt, K.-D., Fuchssteiner, B. (eds.). Functional analysis: Surveys and recent results. I. Amsterdam: North-Holland 1977

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abteilung Mathematik, Universität Dortmund, Postfach 500500, D-4600, Dortmund 50, Federal Republic of Germany

    Hans-Joachim Petzsche

Authors
  1. Hans-Joachim Petzsche
    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

Petzsche, HJ. On E. Borel's theorem. Math. Ann. 282, 299–313 (1988). https://doi.org/10.1007/BF01456977

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01456977

Search

Navigation