Corrigendum to "Center Manifolds without a Phase Space"

We correct the choice of cut-off function in our construction of center manifolds in [G. Faye and A. Scheel, \textit{Trans. Amer. Math. Soc.}, 370 (2018), pp. 5843--5885]. The main result there establishes center manifolds for systems of nonlinear functional equations posed on the real line with nonlocal coupling through convolution operators. In the construction, we need to modify the nonlinearity such that it maps spaces of exponentially growing functions into itself and possesses a small Lipschitz constant. The cut-off function presented there is suitable for $L^\infty$-based construction but insufficient for the choice of $H^1$-spaces. We correct this choice and demonstrate the effect on a pointwise superposition nonlinearity.