Refinement equations and distributional fixed points

摘要

Connections between L1-solutions of the refinement equation of the form f(x)=∫Ω|L|f(Lx-M)dP and distributional fixed points of a special random affine map are investigated. Using results on convergence of perpetuities the direct form of the Fourier transform of L1-solutions of the above refinement equation is obtained.