Infinitesimal operator

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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).

How to Cite This Entry:
Infinitesimal operator. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098