Schwartz functions on Nash manifolds

Abstract

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.

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

References in corpus (1)

• (GL(n+1,F),GL(n,F)) is a Gelfand pair for any local field F

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