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 \(n>1)\) (Q1088271)
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scientific article; zbMATH DE number 3990496
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 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 \(n>1)\) |
scientific article; zbMATH DE number 3990496 |
Statements
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 \(n>1)\) (English)
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1986
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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).
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conformal-Cauchy type distributions
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