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A Green’s function for non-homogeneous random walks on free products. (English) Zbl 0638.60010
For \(\Gamma\) the free product of N groups each having finite orders and a non-homogeneous function \(\alpha\) supported entirely on words of length one in \(\Gamma\), a Green’s function corresponding to \(\alpha\) is developed. The L 2-spectrum of \(\alpha\) is completely developed for the case \(N=2\) and is characterized in general. A method of developing the recursion coefficients of the orthogonal polynomials associated with \(\alpha\) is explored as are the associated spherical functions.
Reviewer: A.R.Trenholme

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60G50 Sums of independent random variables; random walks
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