论文标题
d'Anembert功能方程的变体
A variant of d'Alembert functional equation on monoids
论文作者
论文摘要
在本文中，我们确定功能方程式的复杂值$ f（xσ（y））+f（τ（y）x）= 2f（x）f（x）f（x）f（y）$$对于所有$ x，y \ in m $ in m $ in m $，其中$ m $是单型，$σ$：$σ$：$ m \ longright rondrow and $ $ $ $ $ $ $ $ $ $ m，$ $ m，$ m。反自动形态。该解决方案是根据乘法功能表示的，以及$ 2 $维的不可约合表示$ M $的字符。
In this paper, we determine the complex-valued solutions of the functional equation $$ f(xσ(y))+f(τ(y)x)=2f(x)f(y)$$ for all $x,y \in M$, where $M$ is a monoid, $σ$: $M\longrightarrow M$ is an involutive automorphism and $τ$: $M\longrightarrow M$ is an involutive anti-automorphism. The solutions are expressed in terms of multiplicative functions, and characters of $2$-dimensional irreducible representations of $M$.
