论文标题
在一个和几个变量中的popoviciu-ionescu功能方程
On Popoviciu-Ionescu functional equation in one and several variables
论文作者
论文摘要
我们研究了1955年T. popoviciu最初提出的功能方程。在一维的情况下，它是Ionescu在1956年最容易的情况下解决的，而对于一般情况下，Ghiorcoiasiu和Roscau和Radó于1962年解决了它。我们在范围内均基于一个方程式。在更高维度的设置中分布。对于单个变量的函数，我们的解决方案与现有变量不同，对于几个变量的函数，据我们所知，我们的解决方案是存在的第一个。一维部分已经出现在作者的上一篇论文中。实际上，本文只是对论文Arxiv的一维部分的重新讲述：1604.00616，加入了专门用于在高于一个方面的方程式求解方程的参数。
We study a functional equation first proposed by T. Popoviciu in 1955. In the one-dimensional case, it was solved for the easiest case by Ionescu in 1956 and, for the general case, by Ghiorcoiasiu and Roscau and Radó in 1962. We present a solution to the equation both for the one-dimensional and the higher-dimensional cases, which is based on a generalization of Radó's theorem to distributions in a higher dimensional setting. For functions of a single variable, our solution is different from the existing ones and, for functions of several variables, our solution is, as far as we know, the first one that exists. The one-dimensional part already appeared in a previous paper by the author. Indeed, this paper is just a re-statement of the one-dimensional part of the paper Arxiv:1604.00616, with the addition of the arguments devoted to solve the equation in dimensions higher than one.
