Higher order Fourier analysis

Traditionally,Fourieranalysishasbeenfocusedtheanalysisoffunc-tionsintermsoflinearphasefunctionssuchasthesequencen!e(n)=e2in.Inrecentyears,though,applicationshavearisen-particularlyinconnectionwithproblemsinvolvinglinearpatternssuchasarithmeticprogressions-inwhichithasbeennecessary