Abstract
We use the q-Duhamel product to provide a Banach algebra structure to some closed subspaces of the Wiener disk-algebra W+ (D) of analytic functions on the unit disk D of the complex plane C. We study the q -integration operator on W+ (D) , namely, we characterize invariant subspaces of this operator and describe its extended eigenvalues and extended eigenvectors. Moreover, we prove an addition formula for the spectral multiplicity of the direct sum of q -integration operator on W+ (D) and some Banach space operator.