Resumen:
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The set of all continuous functions with compact supports from a locally compact topological group G to a normed A-module X (A being a normed ring) is denoted by K(G,X). In this work the author characterizes all A-linear maps ?:K(G,X)?X satisfying the two conditions stated below: (1) for compact K?G, there exists a positive constant MK such that ??(f)??MKsups?G?f(s)? for all f?K(G,K) with Supp f?K; (2) ?(sf)=?(f), s?G, for all f?K(G,X), where sf is the function defined by sf(t)=f(s?1t). Theorems of the following type that generalize the uniqueness theorem for Haar measure are also obtained: There exists a ?:K(G,X)?X satisfying conditions (1) and (2) such that every ? of the same kind has the form T??, where T is a bounded A-linear map from X to X. These results are easily generalized to the case in which X is a locally convex Hausdorff topological vector space over R or C.
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