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In this paper, we define β-Hausdorff operator on the unit polydisk
and study the boundedness of the operator on Lipschitz space. Firstly, we
translate the problem of coefficient into integral of weighted composition operator, then give the sufficient conditions of boundedness, and also obtain
an upper bound for the operator norm on Lipschitz space.
We study two particle quantum walks on one dimensional chain. Probability distribution of two particle quantum walks is dependent on the initial state, and symmetric quantum walk or asymmetric quantum walk is analogous to that of one particle quantum walk. The quantum correlation probability is much different from classical coincidence probability. The difference reflects quantum interference between two particles.