On solutions of functional equations determining subsemigroups of $L^1_4$
Colloquium Mathematicum, Tome 119 (2010) no. 2, pp. 181-192
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
group jets zero diffeomorphisms mathbb identifying jets sequences derivatives determine subsemigroups consisting quadruples mathbb setminus times mathbb continuous functions colon mathbb setminus times mathbb mathbb amounts solving set functional equations
Affiliations des auteurs :
Janina Chodukowska 1 ; Zbigniew Marciniak 2
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author = {Janina Chodukowska and Zbigniew Marciniak},
title = {On solutions of functional equations determining subsemigroups of $L^1_4$},
journal = {Colloquium Mathematicum},
pages = {181--192},
publisher = {mathdoc},
volume = {119},
number = {2},
year = {2010},
doi = {10.4064/cm119-2-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm119-2-2/}
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Janina Chodukowska; Zbigniew Marciniak. On solutions of functional equations determining subsemigroups of $L^1_4$. Colloquium Mathematicum, Tome 119 (2010) no. 2, pp. 181-192. doi: 10.4064/cm119-2-2
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