Hyper-positive definite functions II: A complete study of branching-Toeplitz operators
Abstract
We introduce and give a more or less complete study of a family of branching-Toeplitz operators on the Hilbert space 2(Tq) indexed by a rooted homogeneous tree Tq of degree q 2. The finite dimensional analogues of such operators form a very natural family of structured sparse matrices called branching-Toeplitz matrices and will also be investigated. The branching-Toeplitz operators/matrices in this paper should be viewed as natural generalizations of the standard Toeplitz operators/matrices. We will apply our results to construct a family of determinantal point processes on homogeneous trees which are branching-type strong stationary stochastic processes.
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