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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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