Homogeneous polynomials on strictly convex domains

Author:
Piotr Kot

Journal:
Proc. Amer. Math. Soc. **135** (2007), 3895-3903

MSC (2000):
Primary 32A05, 32A40

Published electronically:
September 10, 2007

MathSciNet review:
2341939

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a circular, bounded, strictly convex domain with boundary of class . For any compact subset of we construct a sequence of homogeneous polynomials on which are big at each point of . As an application for any circular subset of type we construct a holomorphic function which is square integrable on and such that where denotes unit disc in .

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Additional Information

**Piotr Kot**

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

Email:
pkot@usk.pk.edu.pl

DOI:
https://doi.org/10.1090/S0002-9939-07-08939-3

Keywords:
homogeneous polynomials,
exceptional sets,
highly nonintegrable holomorphic function

Received by editor(s):
September 8, 2005

Received by editor(s) in revised form:
September 20, 2006

Published electronically:
September 10, 2007

Communicated by:
Mei-Chi Shaw

Article copyright:
© Copyright 2007
American Mathematical Society

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