Characterization of polynomials as solutions of certain functional equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Almira, J. M.^1,2 

[1] Univ Murcia, Fac Informat, Dept Ingn & Tecnol Comp, Campus Espinardo, E-30100 Murcia, Spain

[2] Univ Jaen, Dept Matemat, EPS Linares, C Alfonso X el Sabio 28, Linares 23700, Jaen, Spain

关键词: Frechet's theorem;    Polynomials and exponential;    polynomials on abelian groups;    Linear functional equations;    Montel's theorem;    Characterization problems in probability theory;    Generalized functions;   

DOI  :  10.1016/j.jmaa.2017.11.036

来源: Elsevier

【 摘 要 】

In this paper we present several characterizations of ordinary polynomials as the solution sets of certain functional equations related to the equation Sigma(m)(i = 0) f(i)(b(i)x + c(i)y) = Sigma a(i)(y)v(i)(x), where x, y is an element of R-d and b(i), c(i) is an element of GL(d)(C), whose solution set is, typically, formed by exponential polynomials. Some of these equations are important because of their connection with the Characterization Problem of distributions in Probability Theory.

【 授权许可】

Free