Mathematical Sciences: Harmonic Analysis, Special Functions and Separation of Variables

首席研究员将继续研究各种基本偏微分方程和q-差分方程的对称性之间的关系，可能分离变量的坐标系以及解分离方程的特殊函数的性质。特别是，首席研究员将确定一个适用于所有偏微分方程系统的变量分离的实际定义。接下来他将研究可分离坐标的内在特征问题。最后，他将确定作为分离方程集的解而出现的特殊函数，并研究它们的性质。

The principal investigator will continue studying the relationship between symmetries of various fundamental partial differential equations and q-difference equations, the coordinate systems in which it is possible to separate variables and the properties of the special functions that solve the separated equations. In particular, the principal investigator will determine a practical definition of variable separation that applies to all systems of partial differential equations. Next he will attack the problem of intrinsic characterization of separable coordinates. Finally he will determine the special functions that arise as solutions of the sets of separated equations and study their properties.