The Asymptotic Behaviour of the Fourier Transform of Orthogonal Polynomials II: L.I.F.S. measures and Quantum Mechanics

We study measures generated by systems of linear iterated functions, their Fourier transforms, and those of their orthogonal polynomials. We characterize the asymptotic behaviours of their discrete and continuous averages. Further related quantities are analyzed, and relevance of this analysis to quantum mechanics is briefly discussed.