## Type-dependent positive definite functions on free products of groups.(English)Zbl 0832.43013

Let $$\{G_i\}_{i \in I}$$ be a family of nontrivial groups and let $$G = *_{i\in I} G_i$$ be their free product in which every element $$x$$ has a unique representation as a reduced word: $$x = g_1 \dots g_n$$, where $$n \geq 0$$, $$g_k \in G_{i_k} - \{e\}$$ and $$i_k \neq i_{k + 1}$$. Put $$t(x) = i_1 \dots i_n$$. A function $$f$$ defined on $$G$$ is called type-dependent if $$f(x)$$ depends only on $$t(x)$$. The author studies type-dependent positive definite functions defined on $$G$$.
Reviewer: B.Basit (Clayton)

### MSC:

 43A99 Abstract harmonic analysis 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
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