论文标题
独特解决方案的必要条件
Necessary and Sufficient Conditions for Unique Solution to Functional Equations of Poincare Type
论文作者
论文摘要
分布方程是表征理论中的重要工具，因为可以将分布的许多特征属性转移到此类方程中。使用一种新颖的自然方法，我们撤退了一个显着的分布方程，其在拉普拉斯 - 斯泰尔杰斯变换方面相应的功能方程是庞加雷类型的。提供方程的必要条件，使其具有具有有限差异的独特分配解决方案。这补充了先前的结果，最多涉及分布解决方案的平均值。此外，还研究了更一般的分布（或功能）方程。
Distributional equation is an important tool in the characterization theory because many characteristic properties of distributions can be transferred to such equations. Using a novel and natural approach, we retreat a remarkable distributional equation whose corresponding functional equation in terms of Laplace-Stieltjes transform is of the Poincare type. The necessary and sufficient conditions for the equation to have a unique distributional solution with finite variance are provided. This complements the previous results which involve at most the mean of the distributional solution. Besides, more general distributional (or functional) equations are investigated as well.
