Multilinear Function Series and Transforms in Free Probability Theory
نویسنده
چکیده
The algebra Mul[[B]] of formal multilinear function series over an algebra B and its quotient SymMul[[B]] are introduced, as well as corresponding operations of formal composition, which are associative. In the setting of Mul[[B]], the unsymmetrized R– and T–transforms of random variables in B–valued noncommutative probability spaces are introduced. These satisfy properties analogous to the usual R– and T–transforms, (the latter being just the reciprocal of the S– transform), but describe all moments of a random variable, not only the symmetric moments. The partially ordered set of noncrossing linked partitions is introduced, and used to prove properties of the unsymmetrized T–transform.
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