An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process

Abstract

A new approach to the evanescent part of a two-dimensional weak-stationary stochastic process with the past given by a half-plane is proceed. The classical result due to Helson and Lowdenslager divides a two-parametric weak-stationary stochastic process into three parts. In this paper we describe the most untouchable one - the evanescent part. Moreover, we point out how this part depends on the shape of the past.