On Faber–Schauder coefficients of continuous functions and divergence of greedy algorighms

We consider relationship between the rate of convergence to zero of the Faber–Schauder coefficients of continuous functions and the behavior of the greedy algorithm. We construct a continuous function $f$ with Faber–Schauder coefficients $|A_n (f)|=O(\log^{-1} n)$ and divergent greedy algorithm.