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math.OA2005★ 3 cited
Multilinear function series and transforms in free probability theory
Ken Dykema
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.…
math.OA2005
On the S-transform over a Banach algebra
Kenneth J. Dykema
The S-transform is shown to satisfy a specific twisted multiplicativity property for free random variables in a B-valued Banach noncommutative probability space, for an arbitrary u…