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 such that is strongly annular and is a solution of a Mahler type of functional equation given by where is an integer and is a polynomial with 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 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.