距离函数小波.第II部分：扩展结果和图解
Distance function wavelets - Part II: Extended results and conjectures
摘要：
报告二是关于距离函数小波（DFW）的扩展结果。首先讨论了分数阶DFW变换与分形几何和分数阶导数的关系，然后简要介绍了离散Helmholtz-Fourier变换。Green第二恒等式可能是发展DFW变换和级数理论框架的一种可供选择的设计。文克勒板方程和伯格方程的核心解决方案被用来创建DFW变换和级数。最有趣的是，我们发现高阶Laplace方程的平移不变单项解可以用来构造非常简单的调和多项式DFW级数。在本研究的大多数情况下，缺乏坚实的数学分析，结果是在猜测状态下直观地获得的。
英文摘要：
Report II is concerned with the extended results of distance function wavelets (DFW). The fractional DFW transforms are first addressed relating to the fractal geometry and fractional derivative, and then, the discrete Helmholtz-Fourier transform is briefly presented. The Green second identity may be an alternative devise in developing the theoretical framework of the DFW transform and series. The kernel solutions of the Winkler plate equation and the Burger's equation are used to create the DFW transforms and series. Most interestingly, it is found that the translation invariant monomial solutions of the high-order Laplace equations can be used to make very simple harmonic polynomial DFW series. In most cases of this study, solid mathematical analysis is missing and results are obtained intuitively in the conjecture status.
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