Weiss derivatives of holomorphic maps

We propose an orthogonal approach to the stable homotopy type of spaces of holomorphic maps to projective space. We study the Weiss towers of the unitary functors of holomorphic and continuous maps to $\mathbb{P}(V)$, and show that the former is polynomial and completely compute the latter. As an application we give a new proof of a stable splitting of Cohen--Cohen--Mann--Milgram.