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Convolution operators in \(A^{-\infty}\) for convex domains. (English) Zbl 1254.32009
Summary: We consider convolution operators in spaces of functions which are holomorphic in a bounded convex domain in \(\mathbb C^n\) and have polynomial growth near its boundary. A characterization of the surjectivity of such operators on the class of all domains is given in terms of lower bounds of the Laplace transformation of the analytic functionals defining the operators.

MSC:
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
46E15 Banach spaces of continuous, differentiable or analytic functions
47B38 Linear operators on function spaces (general)
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