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| Abstract |
Let $ chi $ be the set of all functions $ x colon P_i(G) \rightarrow mathbf{C} $ satisfying the inequality $ mid sum_{i=1}^{n}{{alpha}_i x(p_i)} - x(p)x(q) mid leqq C(x) sup__{g in K(x)} mid sum_{i=1}...^{n} {{alpha}_i p_i(g)} - p(g)q(g) mid $, for every $ n, {alpha}_1, {alpha}_2, ldots , {alpha}_n in mathbf{C} $ and $ p_1, p_2, ldots , p_n, p, q in P_e(G) $, where $ C(x) > 0 $ and $ K(x) $ is a compact subset of $ G $. Then a topological group structure can be defined on $ chi $ so that $ chi $ is isomorphic to $ G $. The inequality can be replaced by $ mid sum_{i=1}^{n}{{alpha}_i x(p_i)} - x(p)x(q) mid leqq sup__{g in G} mid f(g) (sum_{i=1}^{n}{{alpha}_i p_i(g)} - p(g)q(g)) mid $, where $ f = f_x in C_{infty} (G) $.show more
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