Skip to main content

Convergence of formal power series and analytic extension

Special Year Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 1276)

Keywords

  • Formal Power Series
  • Complex Line
  • Plurisubharmonic Function
  • Positive Lebesgue Measure
  • Uniform Algebra

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abhyankar, S.S. and T. Moh, A reduction theorem for divergent series, J. Reine Angew. Math. 241 (1970) 27–33.

    MathSciNet  MATH  Google Scholar 

  2. Alexander, H., Projective capacity. In P: Recent developments in several complex variables, 3–27. J.E. Fornaess, ed., Ann. of Math. studies 100, Princeton Univ. Press, 1981.

    Google Scholar 

  3. Hartogs, F., Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen Math. Ann. 62 (1906) 1–88.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Hörmander, L., An introduction to complex analysis in several variables. North Holland Publ. Co., Amsterdam, 1973.

    MATH  Google Scholar 

  5. Korevaar, J., Polynomial approximation numbers, capacities and extended Green functions for C and C n. In: Proc. fifth Texas symposium on approximation theory (1986) Acad. Press (to appear).

    Google Scholar 

  6. Korevaar, J. and J. Wiegerinck, A representation of mixed derivatives with an application to the edge-of-the-wedge theorem. Nederl. Akad. Wetensch. Proc. Ser. A 88 (1985) 77–86.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Leibowitz, G.M., Lectures on complex function algebras. Scott, Foresman and Co., 1970.

    MATH  Google Scholar 

  8. Levenberg, N. and R.E. Molzon, Convergence sets of formal power series. Preprint, Univ. of Kentucky, 1985.

    Google Scholar 

  9. Levenberg, N. and B.A. Taylor, Comparison of capacities in C n. In: Analyse complexe, 162–172. E. Amar. ea., ed., LNM 1094 Springer, Berlin etc., 1984.

    Google Scholar 

  10. Sibony, N. and P.M. Wong, Some results on global analytic sets. In: Sem. Lelong-Skoda 1978/1979, 221–237. LNM 822 Springer, Berlin etc., 1980.

    Google Scholar 

  11. Sathaye, A., Convergence sets of divergent power series. J. Rine Angew. Math. 283 (1976) 86–98.

    MathSciNet  MATH  Google Scholar 

  12. Siciak, J., Extremal plurisubharmonic functions and capacities in C n. Sophia Kokyoroku in Math. 14, Sophia Univ. Tokyo, 1982.

    Google Scholar 

  13. Stout, E.L., The theory of uniform algebras. Bogden & Quigley, Tarrytown-on-Hudson, NY, 1971.

    MATH  Google Scholar 

  14. Wiegerinck, J., A support theorem for Radon transforms on ® n. Nederl. Akad. Wetensch. Proc. Ser. A 88 (1985) 77–86.

    CrossRef  MATH  Google Scholar 

  15. Wiegerinck, J. and J. Korevaar, A lemma on mixed derivatives and results on holomorphic extension. Nederl. Akad. Wetensch. Proc. Ser. A 88, (1985) 351–362.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Wiegerinck, J. (1987). Convergence of formal power series and analytic extension. In: Berenstein, C.A. (eds) Complex Analysis II. Lecture Notes in Mathematics, vol 1276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078967

Download citation

  • DOI: https://doi.org/10.1007/BFb0078967

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18357-0

  • Online ISBN: 978-3-540-47904-8

  • eBook Packages: Springer Book Archive