（反对）对称多元三角函数及其相应的傅里叶变换
(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
摘要：
研究了四类依赖于n个变量的特殊函数。我们称它们为对称和反对称的多元正弦和余弦函数。它们是作为矩阵的行列式或反行列式给出的，矩阵的元素是一个变量的正弦或余弦函数。这些函数是拉普拉斯算子的本征函数，满足n维欧几里得空间的某个域F的边界处的特定条件。离散和连续正交F的功能在每个家庭，允许一个引入对称和反对称的多元傅立叶变换，涉及对称和反对称的多元正弦和余弦函数。
英文摘要：
Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each. These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space. Discrete and continuous orthogonality on F of the functions within each family, allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms, involving the symmetric and antisymmetric multivariate sine and cosine functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
