{"paper":{"title":"Finite Reflection Groups: Invariant functions and functions of the Invariants in finite class of differentiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gerard Barban\\c{c}on","submitted_at":"2019-06-15T08:18:32Z","abstract_excerpt":"Let $W$ be a finite reflection group. A $W$-invariant function of class~$C^{\\infty}$ may be expressed as a functions of class $C^{\\infty}$ of the basic invariants. In finite class of differentiability, the situation is not this simple. Let~$h$ be the greatest Coxeter number of the irreducible components of $W$ and $P$ be~the Chevalley mapping, if $f$ is an invariant function of class $C^{hr}$, and $F$ is the function of invariants associated by $f=F\\circ P$, then $F$ is of class $C^r$. However if~$F$ is of class $C^r$, in general $f=F\\circ P$ is of class $C^r$ and not of class $C^{hr}$. Here w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06494","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}