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In this work we shall prove new results on the theory of convolution operators on spaces of entire functions. The focus is on hypercyclicity results for convolution operators on spaces of entire functions of a given type and order; and existence and approximation results for convolution equations on spaces of entire functions of a given type and order. In both cases we give a generalmethod to prove new results that recover, as particular cases, several results of the literature. Applications of these more general results are given, including new hypercyclicity results for convolution operators on spaces on entire functions on Cn. [ABSTRACT FROM AUTHOR]

In this article we prove existence and approximation results for convolution equations on the spaces of (s; (r, q))-quasi-nuclear mappings of a given type and order on a Banach space E. As special case this yields results for partial differential equations with constant coefficients for entire functions on finite-dimensional complex Banach spaces. We also prove division theorems for (s;m(r, q))-summing functions of a given type and order, that are essential to prove the existence and approximation results. [ABSTRACT FROM AUTHOR]