论文标题
傅立叶变换的代数方法
An Algebraic Approach to Fourier Transformation
论文作者
论文摘要
从代数的角度描述了傅立叶变换的概念，该角度将自己适用于符号计算中的应用。我们基于给定的海森伯格集团建立代数结构（从一般意义上讲，尼尔夸克群体享有分裂财产）；这尤其包括全范围二元性。确定相应类别中的自由对象，并给出各种示例。作为迈向符号计算的第一步，我们详细研究了两个建设性示例 - 高斯（有和没有多项式因素）和双曲线sepant代数。
The notion of Fourier transformation is described from an algebraic perspective that lends itself to applications in Symbolic Computation. We build the algebraic structures on the basis of a given Heisenberg group (in the general sense of nilquadratic groups enjoying a splitting property); this includes in particular the whole gamut of Pontryagin duality. The free objects in the corresponding categories are determined, and various examples are given. As a first step towards Symbolic Computation, we study two constructive examples in some detail -- the Gaussians (with and without polynomial factors) and the hyperbolic secant algebra.
