Convolution equations on spaces of quasi-nuclear functions of a given type and order

Abstract

In this article we prove existence and approximation results for convolution equations on the spaces of $\left( s;\left( r,q\right) \right) $-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 $\left( s;m\left( r,q\right) \right) $-summing functions of a given type and order, that are essential to prove the existence and approximation results.