A general basis set algorithm for galactic haloes and discs

We present a unified approach to (bi-)orthogonal basis sets for gravitating systems. Central our discussion is the notion of mutual gravitational energy, which gives rise ‘self-energy inner product’ on mass densities. consider first-order differential operator that self-adjoint with respect this product, and prove general theorem conditions under set arises by repeated application operator. then show these are fulfilled all families analytical infinite extent have been discovered date. The new theoretical framework turns out be closely connected Fourier-Mellin transforms, it powerful tool constructing sets. demonstrate deriving isochrone model demonstrating its numerical reliability reproducing known result concerning unstable radial modes.