|
Hyperbolic convexity and the analytic fixed point function
Author(s):
Alexander
Yu.
Solynin
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1181-1186.
MSC (2000):
Primary 30C55, 30F45
Posted:
October 18, 2006
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We answer a question raised by D. Mejía and Ch. Pommerenke by showing that the analytic fixed point function is hyperbolically convex in the unit disc.
References:
-
- 1.
- B. Brown Flinn, Hyperbolic convexity and level sets of analytic functions. Indiana Univ. Math. J. 32 (1983), 831-841. MR 0721566 (85b:30010)
- 2.
- S. Dineen, The Schwarz Lemma. The Claredon Press, Oxford, 1989. MR 1033739 (91f:46064)
- 3.
- V. N. Dubinin, Symmetrization in geometric theory of functions of a complex variable. Uspehi Mat. Nauk 49 (1994), 3-76; English translation in Russian Math. Surveys 49:1 (1994), 1-79. MR 1307130 (96b:30054)
- 4.
- F. P. Gardiner and N. Lakic, Quasiconformal Teichmüller Theory. Mathematical Surveys and Monographs, 76. American Mathematical Society, Providence, RI, 2000. MR 1730906 (2001d:32016)
- 5.
- W. K. Hayman, Subharmonic Functions. Vol. 2. London Mathematical Society Monographs, 20. Academic Press, Inc., London, 1989. MR 1049148 (91f:31001)
- 6.
- V. Jørgensen, On an inequality for hyperbolic measure and its applications in the theory of functions. Math. Scand. 4 (1956), 113-124. MR 0084584 (18:885a)
- 7.
- D. Mejía, Ch. Pommerenke, The analytic point function in the disc. Comput. Methods Funct. Theory 5 (2005), no. 2, 275-229. MR 2205415 (2006j:30006)
- 8.
- D. Mejía, Ch. Pommerenke, The analytic point function II. Preprint.
- 9.
- A. Yu. Solynin, Continuous symmetrization of sets. Zap. Nauchn. Semin. LOMI 185 (1990), 125-139; English translation in J. Soviet Math. 59 (1992), 1214-1221. MR 1097593 (92k:28012)
- 10.
- A. Yu. Solynin, Functional inequalities via polarization. Algebra i Analiz 6 (1996), 148-185; English translation in St. Petersburg Math. J. 8:1 (1997), 1015-1038. MR 1458141 (98e:30001a)
- 11.
- A. Yu. Solynin and M. Vuorinen, Estimates for the hyperbolic metric of the punctured plane and applications. Israel J. Math. 124 (2001), 29-60. MR 1856503 (2002j:30071)
- 12.
- R. Sperb, Maximum Principles and Their Applications. Academic Press, Inc., 1981. MR 0615561 (84a:35033)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
30C55, 30F45
Retrieve articles in all Journals with MSC
(2000):
30C55, 30F45
Additional Information:
Alexander
Yu.
Solynin
Affiliation:
Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409
Email:
alex.solynin@ttu.edu
DOI:
10.1090/S0002-9939-06-08661-8
PII:
S 0002-9939(06)08661-8
Keywords:
Analytic fixed point function,
hyperbolic convexity,
Riemann surface,
hyperbolic metric
Received by editor(s):
November 17, 2005
Posted:
October 18, 2006
Additional Notes:
This research was supported in part by NSF grant DMS-0412908
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Solynin, A. Yu., The analytic fixed point function and its properties, Zap. Nauchn. Sem. POMI 337 (2006), 238-252. (Russian) MR MR2271966
G. Jensen and Ch. Pommerenke, On a function-theoretic ruin problem, Ann. Acad. Sci. Fenn. Math. 32 (2007), 523-543.
Gamal', M. F. , On Toeplitz operators similar to the one-sided shift, Zap. Nauchn. Semin. POMI 345 (2007), 85-104. (Russian)
|
Comments: webmaster@ams.org