On some extremal problems in H p and the prediction ofL p -harmonizable stochastic processes

Abstract

We providesimple andsuccinct solutions to two dual extremal problems in the Hardy spacesHp, and to an aspect of the linear prediction problem for a certain class of discrete and continuous parameter “Lp-harmonizable” stochastic processes, for all 1≦p<∞. Two of the results presented appear new. The methods of proof of the rest of the results provide alternatesimpler andshorter proofs for some earlier known theorems.