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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm155, 37 pages, doi:10.1093/imrn/rnm155 published on January 16, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Schwartz Functions on Nash Manifolds

Avraham Aizenbud and Dmitry Gourevitch

Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, POB 26, Rehovot 76100, Israel

Correspondence: Correspondence to be sent to: dmitry.gourevitch{at}weizmann.ac.il

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 Formula and build some additional tools that are important in representation theory.

Communicated by Prof. Joseph Bernstein


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