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On locally bounded solutions of Schilling's problem

Janusz Morawiec (2001)

Annales Polonici Mathematici

We prove that for some parameters q ∈ (0,1) every solution f:ℝ → ℝ of the functional equation f(qx) = 1/(4q) [f(x-1) + f(x+1) + 2f(x)] which vanishes outside the interval [-q/(1-q),q/(1-q)] and is bounded in a neighbourhood of a point of that interval vanishes everywhere.

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