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Let be a normed linear space. We investigate properties of vector functions of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity is equal to the variation of on . As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.
Soit un espace localement compact. Tout opérateur dissipatif de domaine dense dans est limite d’opérateurs dissipatifs bornés. Ce résultat permet, dans le cas où est un espace homogène, de démontrer que tout opérateur dissipatif, de domaine dense et invariant sur se prolonge en le générateur infinitésimal d’un semi-groupe à contraction invariant sur .À tout opérateur vérifiant le principe du maximum positif sur et de domaine assez riche, on associe un opérateur bilinéaire , appelé...
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