We prove ultradifferentiable Chevelley restriction theorems for a wide range of ultradifferentiable classes. As a special case we find that isotropic functions, i.e., functions defined on the vector space of real symmetric matrices invariant under the action of the special orthogonal group by conjugation, possess some ultradifferentiable regularity if and only if their restriction to diagonal matrices has the same regularity.

中文翻译：

---

超微分Chevalley定理和各向同性函数

我们证明了超微分类别的超微分Chevelley限制定理。作为一种特殊情况，我们发现各向同性函数，即在特殊正交群的作用下通过共轭在不变的实对称矩阵的向量空间上定义的函数，当且仅当它们对对角矩阵的约束相同时，才具有某些超微分正则性。规律性。