欧几里得空间中调和势和单演势的分布表示
Representation of Distributions by Harmonic and Monogenic Potentials in Euclidean Space
摘要：
在Clifford分析的框架下，构造了（m+1）维欧几里得空间上半部分的调和势和单演势链，包括复平面上的对数函数的高维模拟，并计算了它们的分布边值.本文在下半空间中确定了这些势，并研究了它们是否可以通过边界R^m延拓。这是将R^m中分布的双无穷序列表示为上下半空间中单演函数在R^m上的跳跃的一个垫脚石，该序列由狄拉克和希尔伯特-狄拉克算子的正整数幂和负整数幂组成，以这种方式提供了克利福德超函数的一系列有趣的例子。
英文摘要：
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of (m+1)-dimensional Euclidean space was recently constructed, including a higher dimensional analogue of the logarithmic function in the complex plane, and their distributional boundary values were computed. In this paper we determine these potentials in lower half-space, and investigate whether they can be extended through the boundary R^m. This is a stepping stone to the representation of a doubly infinite sequence of distributions in R^m, consisting of positive and negative integer powers of the Dirac and the Hilbert-Dirac operators, as the jump across R^m of monogenic functions in the upper and lower half-spaces, in this way providing a sequence of interesting examples of Clifford hyperfunctions.
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。
