离散卷积算子与细分算子的核
Kernels of discrete convolutions and subdivision operators
AI总结：
研究离散卷积算子的核及偏差分算子的齐次解，证明其必为指数多项式，并探讨多项式空间与多变量多项式公共零点乘性的关系。
摘要：
我们考虑离散卷积算子的核，或等价地，偏差分算子的齐次解，并证明这些解必须是指数多项式。相应的多项式空间直接但略显复杂地与某些多变量多项式公共零点的乘性相关联，这一概念由Gröbner在描述具有常系数偏微分算子的核时引入。这些结果可用于确定静止细分算子的核。
英文摘要：
We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in connected directly though somewhat intricately to the multiplicity of the common zeros of certain multivariate polynomials, a concept introduced by Gröbner in the description of kernels of partial differential operators with constant coefficients. These results can are then used to determine the kernels of stationary subdivision operators as well.
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