ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

Bucharest, Romania 1991 MS Classification: 47, 60, 93 Suciu, Ioan, Institute of Mathematics of the Romanian Academy, Bucharest, Romania, Valuşescu, Ilie, Institute of Mathematics of the Romanian Academy, Bucharest, Romania On a maximal function of a semi-spectral measure Operator valued L^{2}-bounded analytic functions on the unit disc D are considered and specific properties, different from the bounded case are obtained. If E is a Hilbert space and F an L(E)- valued semispectral measure on the unit torus T, by an appropriate factorization theorem, there exists, an outer L^{2} - bounded analytic function Θ(λ) attached to F. The attached function Θ(λ) has some “maximal” properties, and in the particular case of the semispectral measure of a contraction T, there exists an explicit connection between the maximal function and its characteristic function Θ_{T}. An important application of the maximal function is the infinite-variate Wiener filter for prediction, with applications in multitime prediction case.