On the completeness of orbits of a Pommiez operator in weighted (LF)-spaces of entire functions

TL;DR

This paper characterizes cyclic vectors for a Pommiez operator acting on a weighted LF-space of entire functions, especially when the space is a Laplace transform of the dual of germs of holomorphic functions, advancing understanding of operator dynamics.

Contribution

It provides a complete description of cyclic vectors for the Pommiez operator in specific weighted LF-spaces, linking operator theory with complex analysis.

Findings

Identifies cyclic vectors in weighted LF-spaces of entire functions.

Connects the structure of these spaces with Laplace transforms of dual spaces.

Advances the theory of operator dynamics in spaces of entire functions.

Abstract

We describe cyclic vectors for a Pommiez operator on a weighted (LF)-space E of entire functions. The full description is obtained where $E$ is the Laplace transform of the strong dual of the space of all germs of holomorphic functions on a convex locally closed set in the complex plane.