The space of real parts of algebras of Fourier transforms
Sungwoo Suh · Pacific Journal of Mathematics · 1981
Let G be a locally compact abelian group with dual group Γ, and let A denote a closed subalgebra of A(Γ), the algebra of all Fourier transforms of functions in L^G), which separates the points of Γ, and whose members do not all vanish at any one point on Γ.Then Re A Re Ac Re A implies A-A(Γ) if Γ is totally disconnected.