Schröder's equation
Equation for fixed point of functional composition / From Wikipedia, the free encyclopedia
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Not to be confused with Schrödinger's equation.
Schröder's equation,[1][2][3] named after Ernst Schröder, is a functional equation with one independent variable: given the function h, find the function Ψ such that
Schröder's equation is an eigenvalue equation for the composition operator Ch that sends a function f to f(h(.)).
If a is a fixed point of h, meaning h(a) = a, then either Ψ(a) = 0 (or ∞) or s = 1. Thus, provided that Ψ(a) is finite and Ψ′(a) does not vanish or diverge, the eigenvalue s is given by s = h′(a).