Schwartz functions on Nash manifolds

Mathematics – Algebraic Geometry

Scientific paper

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35 pages, LaTex. v3:minor changes + reference to results of duCloux

Scientific paper

10.1093/imrn/rnm155

In this paper we extend the notions of Schwartz functions, tempered functions
and generalized Schwartz functions to Nash (i.e. smooth semi-algebraic)
manifolds. We reprove for this case classically known properties of Schwartz
functions on $R^n$ and build some additional tools which are important in
representation theory.

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