论文标题
在多结多项式上
On polyharmonic polynomials
论文作者
论文摘要
我们研究均质多项式在均质多结多项式空间上的正交投影。为此，我们根据基本解决方案的衍生物$ | x |^{2-n} $或$ \ log log | x | $的开尔文变换来得出同质多项式的分解。我们还考虑了均相多结多项式空间的矢量基础，并研究正交系列的收敛问题。
We study the orthogonal projection of homogeneous polynomials onto the space of homogeneous polyharmonic polynomials. To do this we derive the decomposition of homogeneous polynomials in terms of the Kelvin transform of derivatives of the fundamental solution $|x|^{2-n}$ or $\log |x|$. We consider also the vector bases of the space of homogeneous polyharmonic polynomials and study the problem of convergence of orthogonal series.
