$n$维球面上的方向小波
Directional wavelets on $n$-dimensional spheres
摘要：
在$n$维球面上引入了泊松核的方向导数--方向Poisson小波.它表明，稍加修改，并与另一个小波族，它们是一个容许小波对根据来自近似恒等式理论的定义。我们研究了方向泊松小波的一些性质，如其傅里叶系数的递归公式或明确表示为球面变量的函数（对于某些小波）。我们还推导出一个明确的公式为他们的欧几里得极限。
英文摘要：
Directional Poisson wavelets, being directional derivatives of Poisson kernel, are introduced on $n$-dimensional spheres. It is shown that, slightly modified and together with another wavelet family, they are an admissible wavelet pair according to the definition derived from the theory of approximate identities. We investigate some of the properties of directional Poisson wavelets, such as recursive formulae for their Fourier coefficients or explicit representations as functions of spherical variables (for some of the wavelets). We derive also an explicit formula for their Euclidean limits.
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