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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

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