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On solutions of functional equations determining subsemigroups of L¹₄

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Chodukowska J., Marciniak Z.

Colloquium Mathematicum

2010

tom 119

nr 2

181-192

Let L¹₄ be the group of 4-jets at zero of diffeomorphisms f of ℝ with f(0) = 0. Identifying jets with sequences of derivatives, we determine all subsemigroups of L¹₄ consisting of quadruples (x₁,f(x₁,x₄),g(x₁,x₄),x₄) ∈ (ℝ∖{0}) × ℝ³ with continuous functions f,g:(ℝ∖{0}) × ℝ → ℝ. This amounts to solving a set of functional equations.