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Convolution operators on holomorphic Dirichlet series. (English) Zbl 0908.47026
Summary: The present note deals with convolution operators \({\mathcal L}_\mu\) on the class of holomorphic multiple Dirichlet series in bounded convex domains in \(\mathbb{C}^n\). A surjectivity criterion for this operator is obtained. Moreover, the explicit formula for a particular solution \(c\) of the equation \({\mathcal L}_\mu c=d\) for a given right-hand side \(d\) is given.

MSC:
47B38 Linear operators on function spaces (general)
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
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