关于Yamamuro逆定理和隐函数定理的标定
On Yamamuro's inverse and implicit function theorems in terms of calibrations
摘要：
对Frechet空间E=C^{ \infty }（S^1）和光滑的R：R到R，我们证明了x映射到\circ x的伴随映射E到E满足Yamamuro的反函数定理中的连续BΓ-可微条件，仅当R是仿射的.通过较复杂的例子，我们也一般地讨论了用这类简单映射检验所提出的逆函数和隐函数定理的适用性的重要性。
英文摘要：
For the Frechet space E=C^{\infty}(S^1) and for a smooth ϕ: R to R, we prove that the associated map E to E given by x mapstoϕ\circ x satisfies the continuous BΓ--differentiability condition in Yamamuro's inverse function theorem only if ϕis affine. Via more complicated examples, we also generally discuss the importance of testing the applicability of proposed inverse and implicit function theorems by this kind of simple maps.
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