Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Linear independence of iterates of entire functions

Author: Luis Bernal González
Journal: Proc. Amer. Math. Soc. 112 (1991), 1033-1036
MSC: Primary 30D05
MathSciNet review: 1045136
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Abstract: We prove the following result: The set $ \left\{ {{h_n}:n = 0,1, \ldots } \right\}$ is a linearly independent sequence of entire functions, where $ {h_0} = 1,{h_1} = {g_{1,}}{h_2} = {g_1} \circ {g_2},{h_3} = {g_1} \circ {g_2} \circ {g_3}, \ldots ,{g_1}$ is a nonconstant entire function and $ {g_n}(n \geq 2)$ are entire functions which are not polynomials of degree $ \leq 1$. Our theorem generalizes a previous one about linear independence of iterates.

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Keywords: Entire functions, linear independence, iterates, maximum modulus, asymptotic inequalities, composite functions
Article copyright: © Copyright 1991 American Mathematical Society