超可微性的非线性条件：一种统一方法
Nonlinear conditions for ultradifferentiability: a uniform approach
摘要：
最近的工作表明，一个定理的Joris（即一个功能$f$是光滑的，如果两个互质权力的$f$是光滑的）是有效的各种各样的超可微类$\mathcal C$。证明的核心本质上是$1$维的。在某些情况下，一个多维的版本导致微妙的减少参数，但一般的有效性，特别是在准分析设置，仍然是开放的。在本文中，我们给出了一个统一的证明，适用于所有情况和尺寸。它甚至在无限维巴拿赫空间和方便的向量空间上也得到了这个结果。我们还考虑了更一般的非线性条件，即一般的解析芽$Φ$而不是权力，并刻画当$Φ\circ f \in \mathcal C$意味着$f \in \mathcal C$。
英文摘要：
Recent work showed that a theorem of Joris (that a function $f$ is smooth if two coprime powers of $f$ are smooth) is valid in a wide variety of ultradifferentiable classes $\mathcal C$. The core of the proof was essentially $1$-dimensional. In certain cases a multidimensional version resulted from subtle reduction arguments, but general validity, notably in the quasianalytic setting, remained open. In this paper we give a uniform proof which works in all cases and dimensions. It yields the result even on infinite dimensional Banach spaces and convenient vector spaces. We also consider more general nonlinear conditions, namely general analytic germs $Φ$ instead of the powers, and characterize when $Φ\circ f \in \mathcal C$ implies $f \in \mathcal C$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
