Bases in the spaces of Whitney jets (Q2073156)

The author deals with the problem of existence of a basis in spaces \(\mathcal{E}(K)\) of Whitney jets, where \(K\subset \mathbb{R}\) is a compact set of the form \(K=\{(a_k): k\in\mathbb{N}\}\cup\{0\}\), with \(\lim_k a_k=0\). The main result states that \(\mathcal{E}(K)\) admits a Schauder basis whenever \(a_k=e^{-\varphi(k)}\) for a function \(\varphi\) of subexponential growth satisfying certain mild conditions of regularity. This family includes geometric progressions.