泛函方程与Poincare不变力学系统
Functional Equations and Poincare Invariant Mechanical Systems
摘要：
我们研究了在庞加莱代数下力学系统不变的情况下出现的下列函数方程：\sum \limits_{i=1}^{n+1} \dfrac{\partial}{\partial x_{i}} \prod \limits_{j\neq i} f（x_{i} - x_{j}）=0，\qquad n \geq 2。发展了新的技巧，并给出了在某类函数范围内的一般解。找到了新的解决方案。
英文摘要：
We study the following functional equation that has arisen in the context of mechanical systems invariant under the Poincare algebra: \sum\limits_{i=1}^{n+1}\dfrac{\partial}{\partial x_{i}}\prod\limits_{j\neq i}f(x_{i}-x_{j}) =0,\qquad n \geq 2. New techniques are developed and the general solution within a certain class of functions is given. New solutions are found.
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。
