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中文摘要：
在这篇论文，我们在 R~d 在一些 non-tensorproduct 领域上建议著名 Fourier 方法，包括单一、所谓超级单一它由组成(d + 1 )! 笨人 lices。作为二个例子，在 2-D 和 3-D 大小写一超级单一分别地作为平行等边六角形和平行四边的十二面体被显示出。我们扩大了大多数概念和传统的 Fourier 方法的结果在上多变量盒子例如 Fourier 基础系统，傅里叶级数，分离 Fourier 变换( DFT )和它的快算法(快速傅里叶变换)在上超级单一，以及概括正弦和余弦变换( DST ， DCT )并且相关快算法在上一单一。在在这些域上的一个像拉普拉斯算符的操作符的基本直角的系统和特徵函数之间的 Therelationship 被探索。
英文摘要：
In this paper we propose the well-known Fourier method on some non-tensor product domains in Rd, including simplex and so-called super-simplex which consists of （d ＋ 1）! simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a parallel hexagon and a parallel quadrilateral dodecahedron, respectively. We have extended most of concepts and results of the traditional Fourier methods on multivariate cases, such as Fourier basis system, Fourier series, discrete Fourier transform （DFT） and its fast algorithm （FFT） on the super-simplex, as well as generalized sine and cosine transforms （DST, DCT） and related fast algorithms over a simplex. The relationship between the basic orthogonal system and eigen-functions of a LaDlacian-like operator over these domains is explored.
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