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A note on de Branges' weights
Author(s):
Arcadii
Z.
Grinshpan;
Anatolii
Grinshpan
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2605-2608.
MSC (2000):
Primary 30C50, 30C55, 30C75
Posted:
March 31, 2005
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Abstract:
We discuss the de Branges weight systems and give a counterexample uncovering pitfalls.
References:
-
- 1.
- L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), no. 1-2, 137-152. MR 0772434 (86h:30026)
- 2.
- P. Duren, Univalent functions, Springer-Verlag, New York, 1983. MR 0708494 (85j:30034)
- 3.
- A. Grinshpan, Monotone functions of certain motions, preprint, Cal Tech, 2003.
- 4.
- A. Z. Grinshpan, Logarithmic geometry, exponentiation, and coefficient bounds in the theory of univalent functions and nonoverlapping domains, Handbook of Complex Analysis: Geometric Function Theory, V. 1 (Ed. by R. Kühnau), 273-332, North-Holland, Amsterdam, 2002. MR 1966197 (2003m:30041)
- 5.
- A.C. Schaeffer and D.C. Spencer, The coefficients of schlicht functions, Duke Math. J. 10 (1943), 611-635. MR 0009631 (5:175i)
- 6.
- Xie Ming-Qin, A generalization of the de Branges theorem, Proc. of the AMS 125 (1997), no. 12, 3605-3611. MR 1415355 (98b:30018)
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Additional Information:
Arcadii
Z.
Grinshpan
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620
Email:
azg@math.usf.edu
Anatolii
Grinshpan
Affiliation:
Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
Address at time of publication:
Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-1058
Email:
agrinsh@math.okstate.edu
DOI:
10.1090/S0002-9939-05-07934-7
PII:
S 0002-9939(05)07934-7
Keywords:
Univalent functions,
de Branges' weight systems,
associated Legendre functions
Received by editor(s):
January 6, 2004
Posted:
March 31, 2005
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2005,
American Mathematical Society
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