Schwartz Functions on Nash Manifolds

By Avraham Aizenbud, D. Gourevitch. 2007

122 citations recorded by the source corpus.

The goal of 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 the classically known properties of Schwartz functions on and build some additional tools that are important in representation theory.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9e427431c6f22b4a9d3447aaa0ff4cd04dc78e7b

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Multiplicity one theorem for (GL_n+1 (R), GL_n(R)) (2008, methodology): “ manifolds. Our proof of Theorem A widely uses Fourier transform which cannot be applied to general distributions. For this we require a theory of Schwartz functions and distributions as developed in [AG1]. This theory is developed for Nash manifolds. Nash manifolds are smooth semi-algebraic manifol”
Generalized Harish-Chandra descent, Gelfand pairs, and an Archimedean analog of Jacquet-Rallis's theorem (2008, methodology): “wartz distributions on Nash manifolds B.1. Preliminaries and notation. In this appendix we will provesome propertiesof K-equivariantSchwartzdistributions on Nash manifolds. We work in the notation of [AG08a], where one can read about Nash manifolds and Schwartz distributions over them. More detailed”
Multiplicity one theorems: the Archimedean case (2009, methodology): “pered generalized functions on M. We refer the interested reader to [Sh, AG1 ] on generalities of Nash manifolds and tempered generalized functions.”