An Exact Renormalization Formula for the Maryland Model

Abstract

We discuss the difference Schrödinger equation (Formula presented.), (Formula presented.), where (Formula presented.), (Formula presented.) and E are parameters. We obtain explicit renormalization formulas relating its solutions for large (Formula presented.) to solutions of the equation with new parameters (Formula presented.), (Formula presented.) and E for bounded (Formula presented.). These formulas are similar to the renormalization formulas from the theory of Gaussian exponential sums.