On the renewal of a Wiener field on a plane with the use of its values on closed curves

Forw(u, v), (u, v)∉ γ (here,w(x, y), x≥0, y≥0, is a Wiener field and γ is a certain closed curve on a plane), we construct the best mean-square estimate on the basis of the values ofw(x, y) for (x, y)∈ γ. We also calculate the error of this estimate. Donetsk University, Donetsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 744–752, June, 1999.