Seul le groupe des similitudes-inversions préserve le type de la loi de Cauchy-conforme de \({\mathbb{R}}^ n\) pour \(n>1\). (Only the group of similitude-inversions preserves the Cauchy-conformal type distributions of \({\mathbb{R}}^ n\) for \(n>1)\)
On \({\mathbb{R}}^ n\), \(n\geq 2\) the conformal-Cauchy type distributions are introduced. It is proved that a measurable transform \(F: {\mathbb{R}}^ n\to {\mathbb{R}}^ n\) preserves this type iff it coincides almost everywhere with either a similitude or an inversion-similitude of \({\mathbb{R}}^ n\). For the case \(n=1\) see the author, Proc. Am. Math. Soc. 67(1977), 277-286 (1978; Zbl 0376.28019).
scientific article; zbMATH DE number 3990496