指数函数和余弦函数的二维对称和反对称推广
Two-dimensional symmetric and antisymmetric generalizations of exponential and cosine functions
摘要：
本文研究了最近引进的四类双实变量特殊函数的性质，分别记为$E^\pm$和$\cos^\pm$。上标$^+$和$^-$分别表示对称函数和反对称函数。这些功能被认为是在所有的细节需要他们的开发在傅立叶展开的数字数据，采样在正方形网格的任何密度和一般位置的网格在真正的平面相对于晶格定义的基础群论。研究了离散展开式引起的连续插值的性质，并对几种模型函数进行了举例和比较。
英文摘要：
Properties of the four families of recently introduced special functions of two real variables, denoted here by $E^\pm$, and $\cos^\pm$, are studied. The superscripts $^+$ and $^-$ refer to the symmetric and antisymmetric functions respectively. The functions are considered in all details required for their exploitation in Fourier expansions of digital data, sampled on square grids of any density and for general position of the grid in the real plane relative to the lattice defined by the underlying group theory. Quality of continuous interpolation, resulting from the discrete expansions, is studied, exemplified and compared for some model functions.
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