Some Applications of a Convenient Finite-Dimensional Matrix Representation of the Differential Operator

摘要

Representations of the (multiplicative) operator X and the corresponding linear differential operator (D O), d/dx projected into polynomials space with one variable, are considered. It is proved that all polynomial solutions of linear D O of finite order generate one polynomial solution into representation. Polynomial interpolation of functions and spectral analysis of D O are related to those representations.