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On the analytic approximation of differentiable functions from above

Alessandro Tancredi, Alberto Tognoli (2002)

Bollettino dell'Unione Matematica Italiana

We determine conditions in order that a differentiable function be approximable from above by analytic functions, being left invariate on a fixed analytic subset which is a locally complete intersection.

On the group of real analytic diffeomorphisms

Takashi Tsuboi (2009)

Annales scientifiques de l'École Normale Supérieure

The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the n -dimensional torus, its identity component is a simple group. For U ( 1 ) fibered manifolds, for manifolds admitting special semi-free U ( 1 ) actions and for 2- or 3-dimensional manifolds with nontrivial U ( 1 ) actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.

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