科研之友
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摘要
In this article, we aim at characterizing operators acting on functionals of discrete-time normal martingales. Let be a discrete-time normal martingale that has the chaotic representation property. We first introduce a transform, called 2D-Fock transform, for operators from the testing functional space to the generalized functional space of M. Then we characterize continuous linear operators from via their 2D-Fock transforms. Our characterization theorems show that there exists a one-to-one correspondence between continuous linear operators from and functions on x that only satisfy some type of growth condition, where designates the finite power set of Finally, we give some applications of our characterization theorems.
