Skip to main content
SpringerLink
Log in

When is a C∞ function analytic?

  • Article
  • Published:
The Mathematical Intelligencer 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. R. P. Boas, A theorem on analytic functions of a real variable,Bull. Amer. Math. Soc. 41 (1935), 233–236.

    Article  MathSciNet  Google Scholar 

  2. A. Boghossian and P. D. Johnson, Jr., Pointwise conditons for analyticity and polynomiality of infinitely differentiable functions,J. Math. Analysis and Appl. 140 (1989), 301–309.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. J. Hoffman and R. Katz, The sequence of derivatives of a C∞-function,Amer. Math. Monthly 90 (1983), 557–560.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Kolar and J. Fischer, On the validity and practical applicability of derivative analyticity relations,J. Math. Phys. 25 (1984), 2538–2544.

    Article  MathSciNet  Google Scholar 

  5. W. F. Osgood,Lehrbuch der Funktionentheorie, vol. I, 5th. ed., Leipzig and Berlin: Teubner (1928).

    Google Scholar 

  6. A. Pringsheim, Zur Theorie der Taylor’schen Reihe und der analytischen Funktionen mit beschränktem Existenzbereich,Math. Ann. 42 (1893), 153–184.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. Salzmann and K. Zeller, Singularitäten unendlich oft differenzierbarer Funktionen,Math. Z. 62 (1955), 354–367.

    Article  MATH  MathSciNet  Google Scholar 

  8. I. Vrkoc, Holomorphic extension of a function whose odd derivatives are summable,Czechoslovak Math. J. 35(110) (1985), 59–65.

    MathSciNet  Google Scholar 

  9. Z. Zahorski, Sur l’ensemble des points singuliers d’une fonction d’une variable réelle admettant les dérivées de tous les ordres,Fund. Math. 34 (1947), 183–245; supplement,ibid. 36 (1949), 319–320.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Northwestern University, 60208, Evanston, IL, USA

    R. P. Boas

Authors
  1. R. P. Boas
    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

Boas, R.P. When is a C∞ function analytic?. The Mathematical Intelligencer 11, 34–37 (1989). https://doi.org/10.1007/BF03025882

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03025882

Keywords

Search

Navigation