Major Papers


Functional Equations, D'Alembert Functions, Abelian


This major paper is devoted to the study of pre-d'Alembert functions and d'Alembert functions on groups.

In this paper, we first study additive and multiplicative Cauchy equations and the sine addition formula on groups. Then we discuss some properties ofpre-d'Alembert functions on groups. In particular, we characterize when a pre-d'Alembert function is abelian, and furthermore get the general form of abelian pre-d'Alembert functions on groups. Finally we achieve our goal: we obtain the structure of the solution by group representation theory.

Primary Advisor

Dilian Yang

Program Reader

Zhiguo Hu

Degree Name

Master of Science


Mathematics and Statistics

Document Type

Major Research Paper

Convocation Year


Included in

Analysis Commons