Existence of Nontrivial Solutions of Linear Functional Equations
نویسنده
چکیده
In this paper we study functional equation n ∑ i=1 aif(bix+ cih) = 0 (x, h ∈ C) where ai, bi, ci are fixed complex numbers and f : C → C is the unknown function. We show, that if there is an i such that bi/ci ̸= bj/cj holds for any 1 ≤ j ≤ n, j ̸= i, the functional equation has a noncontant solution if and only if there are field automorphisms φ1, . . . , φk of C such that φ1 · . . . · φk is a solution of the equation.
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تاریخ انتشار 2014