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Existence of nontrivial solutions of linear functional equations.
- Source :
- Aequationes Mathematicae; Sep2014, Vol. 88 Issue 1/2, p151-162, 12p
- Publication Year :
- 2014
-
Abstract
- In this paper we study the functional equation where a, b, c are fixed complex numbers and $${f \colon \mathbb{C} \to \mathbb{C}}$$ is the unknown function. We show, that if there is i such that $${b_i / c_i \neq b_j /c_j}$$ holds for any $${1 \leq j \leq n,\ j \neq i}$$ , the functional equation has a nonconstant solution if and only if there are field automorphisms $${\phi_1, \ldots, \phi_k}$$ of $${\mathbb{C}}$$ such that $${\phi_1 \cdots \phi_k}$$ is a solution of the equation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 88
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 97623516
- Full Text :
- https://doi.org/10.1007/s00010-013-0212-z