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arXiv · 2001.06179

Hyper-positive definite functions II: A complete study of branching-Toeplitz operators

Yanqi Qiu·Zipeng Wang
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Abstract

We introduce and give a more or less complete study of a family of branching-Toeplitz operators on the Hilbert space $\ell^2(T_q)$ indexed by a rooted homogeneous tree $T_q$ of degree $q\ge 2$. 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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Yanqi Qiu, Zipeng Wang. 2020-01-17. Hyper-positive definite functions II: A complete study of branching-Toeplitz operators. https://arxiv.org/abs/2001.06179

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