可定义流形上的回火分布与Schwartz函数
Tempered distributions and Schwartz functions on definable manifolds
摘要：
我们定义的空间的施瓦茨函数，回火函数和回火分布的流形上定义的多项式有界的O-极小结构。我们表明，所有的经典性质，这些空间中的纳什范畴，作为第一次研究在福克杜Cloux的工作，也持有在这个广义的设置。我们还表明，流形上定义的O-最小结构，不是多项式有界的，这样的理论不能构建。我们提出了一些可能的应用，主要是在表示论。
英文摘要：
We define the spaces of Schwartz functions, tempered functions and tempered distributions on manifolds definable in polynomially bounded o-minimal structures. We show that all the classical properties that these spaces have in the Nash category, as first studied in Fokko du Cloux's work, also hold in this generalized setting. We also show that on manifolds definable in o-minimal structures that are not polynomially bounded, such a theory can not be constructed. We present some possible applications, mainly in representation theory.
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