Local invertibility and Lie group of superposition operators on harmonic Fock spaces

We investigate various properties of the superposition operator on harmonic Fock spaces. First, we show the operator admits a nontrivial order‐bounded structure only when it acts on the growth‐type harmonic Fock space . Next, we establish several local invertibility conditions that ensure the operator's global invertibility on the spaces. Building on these results, we analyze the group of homeomorphisms and the Lie group generated by the operators and characterize the closed subspaces that remain invariant under the action of the group.