On the approximation of functions on a Hodge manifold

TL;DR

This paper introduces a method to approximate smooth functions on Hodge manifolds using a sequence of algebraic functions inspired by Berezin-Toeplitz quantization, with convergence proven via existing results.

Contribution

It provides a canonical sequence of algebraic functions approximating smooth functions on Hodge manifolds, connecting geometric quantization with function approximation.

Findings

Sequence converges in the smooth topology

Approximants are constructed canonically

Proof leverages known results from Fine, Liu, and Ma

Abstract

If f is a smooth function on a Hodge manifold, we construct a canonical sequence of real algebraic functions that converge to f in the smooth topology. The definition of of the approximants is inspired by Berezin-Toeplitz quantization. The proof follows quickly from known results of Fine, Liu and Ma.