Interpolation and Differentiation for Periodic Functions

摘要

Representation of the (multiplicative) operator X and the corresponding differential operator (D O), d/dx projected into spaces of periodic (or antiperiodic) functions of one variable or arbitrary period, are considered. It is proved that all periodic (or antiperiodic of degree even) solutions of degree odd of D O of finite order give one periodic (or antiperiodic) solution of linear D O of the representation. Polynomial interpolation of a function whose values are pre-assigned and a method to compute the eigenvalves of D O are related to this representation.