Abstract
For a given nonzero entire function g: C → C, we study the linear space F(g) of all entire functions f such that
where φ 1, ψ 1,..., φ n , ψ n : C → C. In the case of g ≡ 1, the expansion characterizes quasipolynomials, that is, linear combinations of products of polynomials by exponential functions. (This is a theorem due to Levi-Civita.) As an application, all solutions of a functional equation in the theory of trilinear functional equations are obtained.
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References
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 50, No. 3, pp. 34–46, 2016 Original Russian Text Copyright © by V. A. Bykovskii
Supported by RFBR grant no. 14-01-00203.
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Bykovskii, V.A. Hyperquasipolynomials and their applications. Funct Anal Its Appl 50, 193–203 (2016). https://doi.org/10.1007/s10688-016-0147-y
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DOI: https://doi.org/10.1007/s10688-016-0147-y