200911.1157v1 Higher order Fourier analysis as an algebraic theory II

Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of approximative statements. The present paper is the second part of a paper in which higher order characters and decompositions were intr..