The effects of zeros in the spectrum on the behavior of the variance for an arithmetic-mean estimate of a homogeneous random field

We study the arithmetic-mean estimate of a homogeneous random field observed on a rectangle and, in particular, the asymptotic behavior of the variance of such an estimate when there are zeros in the spectrum of the process.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 70, pp. 137–144, 1990.