The cosine and sine addition and subtraction formulas on semigroups (Q2064771)

As a continuation of his paper [Acta Math. Hung. 164, No. 2, 533--555 (2021; Zbl 1488.39065)], the author finds the general solution \(f,g: S\to \mathbb{C}\) of the cosine addition formula \(g(xy) = g(x)g(y)- f(x)f(y)\), where \(S\) is a semigroup. In addition, he solves the cosine subtraction formula \(g(x\sigma(y)) = g(x)g(y)+ f(x)f(y)\) on monoids when \(\sigma\) is an automorphic involution. Furthermore, he investigates the continuous solutions on topological semigroups.