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On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

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Abstract

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form \({w_1a_1^{z}+w_2a_2^{z}+\cdots+w_na_n^{z}}\), with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of \({\mathbb{C}}\), which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j .

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Authors and Affiliations

  1. Department of Mathematical Analysis, University of Alicante, P.O. Box 99, 03080, Alicante, Spain

    Juan Matías Sepulcre & Tomás Vidal

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  1. Juan Matías Sepulcre
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  2. Tomás Vidal
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Correspondence to Juan Matías Sepulcre.

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Sepulcre, J.M., Vidal, T. On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0. Mediterr. J. Math. 12, 667–678 (2015). https://doi.org/10.1007/s00009-014-0444-8

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  • DOI: https://doi.org/10.1007/s00009-014-0444-8

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