Bounded holomorphic functions with given maximum modulus on all circles

Author:
Piotr Kot

Journal:
Proc. Amer. Math. Soc. **137** (2009), 179-187

MSC (2000):
Primary 32A05, 32A35

Published electronically:
July 31, 2008

MathSciNet review:
2439439

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Abstract: We study , a circular, bounded, strictly convex domain with boundary. Let and be continuous functions on with for and . First we prove that can be approximated by the maximum modulus values of homogeneous polynomials, where is independent from . Next we construct such that

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Additional Information

**Piotr Kot**

Affiliation:
Politechnika Krakowska, Instytut Matematyki, ul. Warszawska 24, 31-155 Kraków, Poland

Email:
pkot@pk.edu.pl

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09468-9

Keywords:
Homogeneous polynomials,
maximum modulus set,
inner function.

Received by editor(s):
September 11, 2007

Received by editor(s) in revised form:
December 12, 2007

Published electronically:
July 31, 2008

Communicated by:
Mei-Chi Shaw

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.