On solutions of functional equations determining subsemigroups of $L^1_4$
Tom 119 / 2010
Colloquium Mathematicum 119 (2010), 181-192
MSC: 39B72, 37C05.
DOI: 10.4064/cm119-2-2
Streszczenie
Let $L_4^1$ be the group of 4-jets at zero of diffeomorphisms $f$ of $\mathbb{R}$ with $f(0)=0$. Identifying jets with sequences of derivatives, we determine all subsemigroups of $L_4^1$ consisting of quadruples $(x_1,f(x_1,x_4),g(x_1,x_4),x_4)\in(\mathbb{R}\setminus\{0\})\times\mathbb{R}^3$ with continuous functions $f,g\colon(\mathbb{R}\setminus\{0\})\times\mathbb{R}\to\mathbb{R}$. This amounts to solving a set of functional equations.
