線性差分方程的可解性

Abstract

這篇論文最主要是在探討關於線性差分方程的可解性。主要是以幾何的觀點去探討關於(E, A, B)-系統的解的性質。我們先以較簡單的(E, A)-系統入手，並且嘗試著利用幾何的觀點去探討出其解的性質。並且希望可以將求解的方式，以與所選取基底無關的方法來獲得相關結論。 而(E, A)-系統為(E, A, B)-系統的特例。因此之後可利用之前的結論，再進一步地研究關於(E, A, B)-系統解的特性。而在最後，也得以完整的描述解空間。

In this thesis, we focus on the solvability of singular linear difference equations. We use the geometric viewpoint to survey the properties about the solutions of (E, A, B)-system. First, we consider the simple system—(E, A)-system. We try to use the geometric technique to solve the properties about the solutions of (E, A)-system. And we hope that we can solve it by the way which is independent of the choice of the basis. And (E, A)-system is a special case of the (E, A, B)-system. So, we can use the conclusions which we got before to solve the solution of the (E, A, B)-system. Finally, we have described the solution space of (E, A, B)-system.