Continuous linear decomposition of analytic functions

Abstract

We prove that continuous linear decomposition operators exist on the space $A(J)$ of real analytic germs and on the space $A(I)$ of real analytic functions where $J$ is a compact interval (and $I$ is an open interval). We then characterize when $A(J)$ and $A(I)$ contain the space $A_{per}(\mathbb{R})$ of $2\pi-$periodic real analytic functions as a complemented subspace. As a further application we present new formulas for continuous linear right inverses for convolution operators on real analytic functions.