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Approximation by strongly annular solutions of functional equations


Author: R. Daquila
Journal: Proc. Amer. Math. Soc. 138 (2010), 2505-2511
MSC (2010): Primary 30D10, 30B30, 30E10, 41A30
DOI: https://doi.org/10.1090/S0002-9939-10-10278-0
Published electronically: February 18, 2010
MathSciNet review: 2607880
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Abstract: A major result of this paper is that the set of all functions $ g(z)$ such that $ g$ is strongly annular and is a solution of a Mahler type of functional equation given by $ g(z)=q(z)g(z^p)$ where $ p\ge 2$ is an integer and $ q$ is a polynomial with $ q(0)=1$ is a dense first category set in the set of all holomorphic functions on the open unit disk with the topology of almost uniform convergence. A second result is that strongly annular solutions of these types of functional equations are dense in the space of holomorphic functions with Maclaurin coefficients of $ \pm 1$ with the same topology.


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Additional Information

R. Daquila
Affiliation: Department of Mathematics, Muskingum University, New Concord, Ohio 43762
Email: rdaquila@muskingum.edu

DOI: https://doi.org/10.1090/S0002-9939-10-10278-0
Received by editor(s): July 31, 2009
Received by editor(s) in revised form: October 20, 2009, and November 5, 2009
Published electronically: February 18, 2010
Communicated by: Walter Van Assche
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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