正弦函数的二维对称和反对称推广
Two dimensional symmetric and antisymmetric generalizations of sine functions
摘要：
描述了关于其两个变量的置换对称或反对称的正弦函数的二维推广的性质。它表明，功能是正交的，当集成在一个有限的区域$F$的真正的欧几里德空间，他们是离散正交的，当总结了在$F$中的任何密度的格。函数的乘积分解为它们的和的可分解性是通过显式分解所有类型的乘积来证明的。建立了$F$中二维格点上数字数据的类傅立叶展开的形式。研究了数字数据的连续插值问题。
英文摘要：
Properties of 2-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutation of their two variables are described. It is shown that the functions are orthogonal when integrated over a finite region $F$ of the real Euclidean space, and that they are discretely orthogonal when summed up over a lattice of any density in $F$. Decomposability of the products of functions into their sums is shown by explicitly decomposing products of all types. The formalism is set up for Fourier-like expansions of digital data over 2-dimensional lattices in $F$. Continuous interpolation of digital data is studied.
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