Description
I review a recent mathematical development (arxiv:2302.06944) in the theory of biorthogonal basis sets, with particular attention given to practical numerical implementation. This work introduces an algorithm, the output of which is a traditional (Clutton-Brock-style) basis set, starting from any reasonable smooth function describing the zeroth-order spherical or disc-like mass density of a chosen stellar system. There follows a discussion of the questions and research prospects raised by this line of work: first, the quest for basis functions whose underlying shape is adapted to more general galaxy geometries (discs, spheroids or ellipsoids). And second, the link between the galactic dynamicists' notion of basis function and the technique of Coulomb resolutions in computational quantum chemistry (an example of parallel development in different branches of science).
