There are four most important functional spaces in analysis:
the space $\mathcal{C}(M)$ of continuous functions on a topological space,
the space $\mathcal{E}(M)$ of smooth functions on a smooth manifold,
the space $\mathcal{O}(M)$ of holomorphic functions on a complex manifold, and
the space $\mathcal{P}(M)$ of polynomials on an algebraic manifold.
In the first two cases the functionals on the spaces have well-known names:
continuous functionals $f:\mathcal{C}(M)\to\mathbb{C}$ are called measures, and
continuous functionals $f:\mathcal{E}(M)\to\mathbb{C}$ are called distributions.
What do people call continuous functionals on $\mathcal{O}(M)$ and on $\mathcal{P}(M)$?
(The space $\mathcal{P}(M)$$\mathcal{O}(M)$ is supposed to be endowed with the strongesusual compact-open topology, and the space $\mathcal{P}(M)$ with the strongest locally convex topology, so each linear functional on it$\mathcal{P}(M)$ is continuous.)
I saw the names analytic functionals for $f:\mathcal{O}(M)\to\mathbb{C}$, and currents for $f:\mathcal{P}(M)\to\mathbb{C}$, but both terms sound strange to me.
Is it possible that there are more or less convenient names for these objects?