具有自同构的余弦与正弦加减律
Cosine and Sine addition and subtraction law with an automorphism
摘要：
设$S$是半群.我们的主要结果是，我们描述了以下函数方程\[g(xσ(y)) = g(x)g(y)+f(x)f(y),\ x,y\in S,\] \[f(xσ(y)) = f(x)g(y)+f(y)g(x),\ x,y\in S,\]和\[f(xσ(y)) = f(x)g(y)-f(y)g(x),\ x,y\in S,\]的复值解，其中$σ:S\rightarrow S$是一个不需要对合的自同构.因此，我们表明，前两个方程是等价的，他们的变种。我们也给出了一些应用。
英文摘要：
Let $S$ be a semigroup. Our main results is that we describe the complex-valued solutions of the following functional equations \[g(xσ(y)) = g(x)g(y)+f(x)f(y),\ x,y\in S,\] \[f(xσ(y)) = f(x)g(y)+f(y)g(x),\ x,y\in S,\] and \[f(xσ(y)) = f(x)g(y)-f(y)g(x),\ x,y\in S,\] where $σ:S\rightarrow S$ is an automorphism that need not be involutive. As a consequence we show that the first two equations are equivalent to their variants. We also give some applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
