Abstract
Let denote the algebra of all n-times continuously differentiable functions on which are holomorphic on the unit disc :. We prove that is a Banach algebra with multiplication as Duhamel product and describe its maximal ideal space. We also describe the commutant and strong cyclic vectors of the integration operator. Using the Duhamel product we also study the extended eigenvalues and the corresponding extended eigenvectors of the integration operator .
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