  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.
