Hadamard Type Operators on Spaces of Holomorphic Functions with Prescribed Behavior Near Boundary

A representation in the form of a multiplicative convolution is obtained for Hadamard type operators on spaces of holomorphic functions on a bounded convex complex domain which have polynomial growth near the boundary of the domain or are infinitely differentiable up to the boundary. It is proved that the spaces of Hadamard type operators under consideration endowed with the topology of uniform convergence on bounded sets are topologically isomorphic to the strong dual of the space of all C^∞ functions on the corresponding set of multipliers holomorphic in its interior.