A Differential Analogue of Favard's Theorem

Arieh Iserles, Marcus Webb

Favard's theorem characterizes bases of functions $\{p_n{\}}_{n\in {\mathbb{Z}}_{+}}$ for which $x{p}_n(x)$ is a linear combination of $p_{n-1}(x)$, $p_n(x)$, and $p_{n+1}(x)$ for all $n \…