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On a functional equation with derivative and symmetrization

Adam Bobrowski; Małgorzata Kubalińska — 2006

Annales Polonici Mathematici

We study existence, uniqueness and form of solutions to the equation $α g - β g^{'} + γ g_{e} = f$ where α, β, γ and f are given, and $g_{e}$ stands for the even part of a searched-for differentiable function g. This equation emerged naturally as a result of the analysis of the distribution of a certain random process modelling a population genetics phenomenon.

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