Abstract:We develop the complex-analytic viewpoint on the tree convolutions studied by the second author and Weihua Liu in [27], which generalize the free, boolean, monotone, and orthogonal convolutions. In particular, for each rooted subtree T of the N -regular tree (with vertices labeled by alternating strings), we define the convolution ⊞ T (µ 1 , . . . , µ N ) for arbitrary probability measures µ 1 , . . . , µ N on R using a certain fixed-point equation for the Cauchy transforms. The convolution operations respect … Show more
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