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The duality theory of topological groups with the convolution of functions. (English) Zbl 1007.43003

The paper contains two theorems (\(G\) is a locally compact abelian group and \(G'\) its dual): (1) Let there exist a function \(f_1\in L_p(G)\). Then there exist two dual measurable functions \(f_1'\) and \(g_1'\) with \(f_1'+g_1'\in L_1(G')\). (2) There exists the result \(f_1'*g_1'\in L_1(G') \Rightarrow x'*y'\in G'\).

MSC:

43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
22A05 Structure of general topological groups
43A07 Means on groups, semigroups, etc.; amenable groups
22B05 General properties and structure of LCA groups
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