General Theory of Linear Functional Equations in the Space of Strictly Monotonic Functions

摘要

The classical theory of k-th order linear functional and difference equations is obtained as a special case of the theory developed here for the k-th order functional equation model which generalizes the first order model f ○ ? ? Af = B. The function ? belongs to a special space S of continuous strictly monotonic functions equipped with a group multiplication ○. The equation's domain can be a finite interval, a half-line or the real line. Announced here are the main theorems on solution structure for k-th order homogeneous linear functional equations in S.