Solution of several functional equations on nonunital semigroups using Wilson's functional equations with involution
Summary: Let \(S\) be a nonunital commutative semigroup, \(\sigma\colon S \to S\) an involution, and \(\mathbb{C}\) the set of complex numbers. In this paper, first we determine the general solutions \(f, g\colon S \to \mathbb{C}\) of Wilson's generalizations of d'Alembert's functional equations \(f(x + y) + f(x + \sigma y) = 2 f(x) g(y)\) and \(f(x + y) + f (x + \sigma y) = 2 g(x) f(y)\) on nonunital commutative semigroups, and then using the solutions of these equations we solve a number of other functional equations on more general domains.
scientific article; zbMATH DE number 7022431