| Popis: |
All paper is related with the non-zero continuous solutions f : G → ℂ of the functional equation f(xσ(y))+f(τ(y)x)=2f(x)f(y), x,y∈G,$${\rm{f}}({\rm{x}}\sigma ({\rm{y}})) + {\rm{f}}(\tau ({\rm{y}}){\rm{x}}) = 2{\rm{f}}({\rm{x}}){\rm{f}}({\rm{y}}),\;\;\;\;\;{\rm{x}},{\rm{y}} \in {\rm{G}},$$ where σ; τ are continuous automorphism or continuous anti-automorphism defined on a compact group G and possibly non-abelian, such that σ2 = τ2 = id: The solutions are given in terms of unitary characters of G: |
