No abstract

Let (Xi, i = 1, 2,. . .) be the normalized gaussian system such that Xi ∈ N (0, 1), i = 1, 2,. .. and let the correlation matrix ρij = E(XiXj) satisfy the following hypothesis: C = sup i≥1 ∞ j=1 |ρi,j| < ∞. We present Gebelein's inequality and some of its consequences: Borel-Cantelli type lemma, iterated log law, Levy's norm for the gaussian sequence etc. The main result is that f (X1) + • • • + f (Xn) n → 0 a.s. for f ∈ L 1 (ν) with (f, 1)ν = 0.

Abstract. We shall study properties of box spline operators: cardinal interpolation, convolution, and the Bernstein-Schnabl operator. We prove the saturation theorem.

No abstract