Vol. 71, No. 1, 1977

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ISSN: 0030-8730
Weakly orthogonally additive functionals, white noise integrals and linear Gaussian stochastic processes

Jan Rosiński and Wojbor Woyczynski

Vol. 71 (1977), No. 1, 159–172
Abstract

Let E be a Banach space. We prove a representation theorem for functionals on L2(E) that are additive on weakly orthogonal elements (as defind by Beck and Warren in Pacific J. Math. in 1972) and utilize the theorem to obtain a characterization theorem for linear Gaussian stochastic processes on L2(E) that take independent values on weakly orthogonal functions. This enables us give a new and very natural interpretation of the notion of weak orthogonality.

Mathematical Subject Classification 2000
Primary: 60B05
Secondary: 46E99, 60G15
Milestones
Received: 12 May 1976
Revised: 26 October 1976
Published: 1 July 1977
Authors
Jan Rosiński
Wojbor Woyczynski