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On a functional equation with derivative and symmetrization. (English) Zbl 1156.34338
Summary: We study existence, uniqueness and form of solutions to the equation αg-βg ' +γg 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.
MSC:
34K06Linear functional-differential equations
92D10Genetics
47D06One-parameter semigroups and linear evolution equations