The uncertainty product of a function is a quantity that measures the trade-off between the space and the frequency localization of the function. Its boundedness from below is the content of various uncertainty principles. In the present paper, functions over the n-dimensional sphere are considered. A formula is derived that expresses the uncertainty product of a continuous function in terms of its Fourier coefficients. It is applied to a directional derivative of a zonal wavelet, and the behavior of the uncertainty product of this function is discussed.

中文翻译：

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关于球面函数的不确定性积

函数的不确定性乘积是一个量度，该量度测量空间与函数的频率局部性之间的平衡。从下面看，它的边界是各种不确定性原理的内容。在本文中，考虑了n维球面上的函数。导出了一个公式，该公式根据傅立叶系数表示连续函数的不确定性乘积。将其应用于带状小波的方向导数，并讨论了该函数的不确定性产物的行为。