JOURNAL BROWSE
Search
Advanced SearchSearch Tips
AN EXTREMAL PROBLEM OF HOLOMORPHIC FUNCTIONS IN THE COMPLEX PLANE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 4,  2013, pp.717-727
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.4.717
 Title & Authors
AN EXTREMAL PROBLEM OF HOLOMORPHIC FUNCTIONS IN THE COMPLEX PLANE
Chung, Young-Bok; Park, Byoung-Il;
  PDF(new window)
 Abstract
In this paper, we study on a higher order extremal problem relating the Ahlfors map associated to the pair of a finitely connected domain in the complex plane and a point there. We show the power of the Ahlfors map with some error term which is conformally equivalent maximizes any higher order derivative of holomorphic functions at the given point in the domain.
 Keywords
extremal;Rieman mapping function;Ahlfors map;kernel function;
 Language
English
 Cited by
 References
1.
Lars V. Ahlfors, Complex analysis. An introduction to the theory of analytic functions of one complex variable, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953.

2.
S. Bell, Solving the Dirichlet problem in the plane by means of the Cauchy integral, Indiana Univ. Math. J. 39(4) (1990), 1355-1371. crossref(new window)

3.
Steve Bell, The Szego projection and the classical objects of potential theory in the plane, Duke Math. J. 64(1) (1991), 1-26. crossref(new window)

4.
Steven R. Bell, The Cauchy transform, potential theory, and conformal mapping, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992.

5.
Steven R. Bell, The fundamental role of the Szego kernel in potential theory and complex analysis, J. Reine Angew. Math. 525 (2000), 1-16.

6.
Y.-B. Chung, The Ahlfors mapping function and an extremal problem in the plane, Houston J. Math. 19 (1993), 263-273.

7.
Young-Bok Chung, Higher order extremal problem and proper holomorphic mapping, Houston J. Math. 27(3) (2001), 707-718.

8.
Zeev Nehari, Conformal mapping, Dover Publications Inc., New York, 1975, Reprinting of the 1952 edition.