Skip to main content
SpringerLink
Log in

The Cauchy kernel, the Szegö kernel, and the Riemann mapping function

  • 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. Ahlfors, L.: Remarks on the Neumann-Poincaré integral equation. Pac. J. of Math.2, 271–280 (1952)

    Google Scholar 

  2. Bergman, S.: The kernel function and conformal mapping. A.M.S. Math. Surveys No. 5 (1970)

  3. Birkhoff, G., Young, D.M., Zarantonello, E.H.: Numerical methods in conformal mapping. Proc. Symp. Appl. Math.4, 117–140 (1953)

    Google Scholar 

  4. Kerzman, N.: A Monge-Ampère equation in complex analysis. Proc. of Symp. Pure Math.30, 161–167 (1977)

    Google Scholar 

  5. Kerzman, N., Stein, E.M.: The Szegö kernel in terms of Cauchy-Fantappiè kernels. Duke Math. Jour., June 78

  6. Kerzman, N., Stein, E.M.: Integral representations and boundary behaviour in several complex variables (Book to appear)

  7. Kolmogoroff, A.N., Fomin, S.V.: Functional analysis. p. 61: Graylock Press 1961

  8. Muskelishvili, N.I.: Singular integral equations. Trl. from Russian. Groningen: Noordhoff 1953

    Google Scholar 

  9. Poincaré, H.: La methode de Neumann et le problème de Dirichlet. Acta Math.20, 59–142 (1895)

    Google Scholar 

  10. Rademacher, H., Toeplitz, O.: The enjoyment of mathematics. Princeton: Princeton University Press 1957

    Google Scholar 

  11. Stein, E.M.: Boundary behaviour of holomorphic functions in several complex variables. Princeton: Princeton University Press 1972

    Google Scholar 

  12. Warschawski, S.: On differentiability at the boundary in conformal mapping. Proc. A.M.S.12, 614–620 (1961)

    Google Scholar 

  13. Zygmund, A.: Trigonometric series. 2nd Ed., 2 Vols. Cambridge: Cambridge University Press 1959

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    N. Kerzman

  2. Princeton University, 08540, Princeton, NJ, USA

    E. M. Stein

Authors
  1. N. Kerzman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. M. Stein
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

We would like to thank Professor L. Ahlfors for useful comments and references.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kerzman, N., Stein, E.M. The Cauchy kernel, the Szegö kernel, and the Riemann mapping function. Math. Ann. 236, 85–93 (1978). https://doi.org/10.1007/BF01420257

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01420257

Keywords

Search

Navigation