1. CMB 2011 (vol 56 pp. 218)
 Yang, Dilian

Functional Equations and Fourier Analysis
By exploring the relations among functional equations, harmonic analysis and representation theory,
we give a unified and very accessible approach to solve three important functional equations 
the d'Alembert equation, the Wilson equation, and the d'Alembert long equation 
on compact groups.
Keywords:functional equations, Fourier analysis, representation of compact groups Categories:39B52, 22C05, 43A30 

2. CMB 2011 (vol 55 pp. 60)
 Coons, Michael

Extension of Some Theorems of W. Schwarz
In this paper, we prove that a nonzero power series $F(z)\in\mathbb{C}
[\mkern3mu[ z]\mkern3mu]
$
satisfying $$F(z^d)=F(z)+\frac{A(z)}{B(z)},$$ where $d\geq 2$, $A(z),B(z)\in\mathbb{C}[z]$
with $A(z)\neq 0$ and $\deg A(z),\deg B(z)
Keywords:functional equations, transcendence, power series Categories:11B37, 11J81 

3. CMB 2005 (vol 48 pp. 505)
 Bouikhalene, Belaid

On the Generalized d'Alembert's and Wilson's Functional Equations on a Compact group
Let $G$ be a compact group. Let $\sigma$ be a continuous involution
of $G$. In this paper, we are
concerned by the following functional equation
$$\int_{G}f(xtyt^{1})\,dt+\int_{G}f(xt\sigma(y)t^{1})\,dt=2g(x)h(y), \quad
x, y \in G,$$ where $f, g, h \colonG \mapsto \mathbb{C}$, to be
determined, are complex continuous functions on $G$ such that $f$ is
central. This equation generalizes d'Alembert's and Wilson's
functional equations. We show that the solutions are expressed by
means of characters of irreducible, continuous and unitary
representations of the group $G$.
Keywords:Compact groups, Functional equations, Central functions, Lie, groups, Invariant differential operators. Categories:39B32, 39B42, 22D10, 22D12, 22D15 
