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

Młotkowski, Wojciech

Colloq. Math. 64, No. 1, 41-54 (1993).

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)

Keywords:

free product; representation; reduced word; type-dependent positive definite functions