Description of Maximal Ideal Space of Some Banach Algebra with Multiplication as Duhamel Product

Abstract

Let denote the vector space of complex-valued functions that are continuous on the closed unit disk  and have nth order derivatives in D, which can be extended to functions continuous on . Let denote the subspace of the functions which are analytic in D. We prove that is a Banach algebra with multiplication as Duhamel product and describe its maximal ideal space. We also describe commutant and strong cyclic vectors of the integration operator