The name for linear operators that are differentials of mappings of certain classes (cf. Differential). Thus, on a differentiable manifold an infinitesimal operator, or infinitesimal transformation, is the same as a vector field; in the theory of semi-groups (of operators, of transformations) it is the same as an (infinitesimal) generating operator (cf. Generating operator of a semi-group).
Infinitesimal operator. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Infinitesimal_operator&oldid=17699