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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Title: 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
Authors: Sepulcre, Juan Matias | Vidal, Tomás
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Functional equations | Complex variable | Exponential polynomials
Knowledge Area: Análisis Matemático
Issue Date: Jul-2015
Publisher: Springer Basel
Citation: Mediterranean Journal of Mathematics. 2015, 12(3): 667-678. doi:10.1007/s00009-014-0444-8
Abstract: In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, 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 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.
URI: http://hdl.handle.net/10045/52994
ISSN: 1660-5446 (Print) | 1660-5454 (Online)
DOI: 10.1007/s00009-014-0444-8
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Springer Basel 2014. The final publication is available at Springer via http://dx.doi.org/10.1007/s00009-014-0444-8
Peer Review: si
Publisher version: http://dx.doi.org/10.1007/s00009-014-0444-8
Appears in Collections:INV - CADAGL - Artículos de Revistas

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