Many authors have studied exponentially-convergent tractability in the worst case setting. But almost all articles related to tractability are focused on the classes of some multivariate functions defined over the unit cubes ${[0,1]}^m$ or ${\mathbb{R}}^m$. Note that simplex is also important in geometry and has many practical applications. In this paper we considered tractability of the approximation problems of function spaces with exponential weights defined over products of simplices and obtained necessary and sufficient conditions for certain kinds of tractability, including EC-tractability.

中文翻译：

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关于单纯形乘积定义的函数空间中的近似问题的EC难处理性

许多作者研究了在最坏情况下的指数收敛性。但是几乎所有与易处理性相关的文章都集中在单位多维数据集上定义的一些多元函数的类上${[0，\mathrm{1个}]}^{米}$ 要么 ${\mathbb{[R}}^{米}$。请注意，单纯形在几何中也很重要，并且有许多实际应用。在本文中，我们考虑了具有指数权重的函数空间逼近问题的可扩展性，其中指数权重定义为单纯形的乘积，并为某些可扩展性（包括EC-可扩展性）获得了必要和充分的条件。