On generators of spaces of entire functions with a system of weighted estimates

We consider spaces of entire functions with systems of weight estimates. The case of binomial weight sequences consisting of radial and nonradial components is investigated. Under some assumptions on the weight sequence we obtain a complete description of generators in these spaces. We apply this result to the problem of normal solvability of systems of convolution equations in the Roumieu spaces of ultradifferentiable functions and, as a particular case, in Gevrey classes.