On an alternative cauchy equation in two unknown functions. Some classes of solutions |
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Authors: | Gian Luigi Forti Luigi Paganoni |
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Affiliation: | (1) Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, I-20133 Milano, Italia |
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Abstract: | Summary In this paper we consider the alternative Cauchy functional equationg(xy) g(x)g(y) impliesf(xy) = f(x)f(y) wheref, g are functions from a topological group (X, ·) into a group (S,·). First we prove that, ifS is a Hausdorff topological group andX satisfies some weak additional hypotheses, then (f, g) is a continuous solution if and only if eitherf org is a homomorphism. Then we describe a more general class of solutions forX =Rn.Partially supported by M.U.R.S.T. Research funds (40%)Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth. |
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Keywords: | Primary 39B30 39B50 39B70 |
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