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# More Eventual Positivity for Analytic Functions

Published:2003-10-01
Printed: Oct 2003
• David Handelman
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## Abstract

Eventual positivity problems for real convergent Maclaurin series lead to density questions for sets of harmonic functions. These are solved for large classes of series, and in so doing, asymptotic estimates are obtained for the values of the series near the radius of convergence and for the coefficients of convolution powers.
 MSC Classifications: 30B10 - Power series (including lacunary series) 30D15 - Special classes of entire functions and growth estimates 30C50 - Coefficient problems for univalent and multivalent functions 13A99 - None of the above, but in this section 41A58 - Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) 42A16 - Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30}