Tempered distributions and Schwartz functions on definable manifolds
Representation Theory
2020-03-12 v3 Functional Analysis
Geometric Topology
Abstract
We define the spaces of Schwartz functions, tempered functions and tempered distributions on manifolds definable in polynomially bounded o-minimal structures. We show that all the classical properties that these spaces have in the Nash category, as first studied in Fokko du Cloux's work, also hold in this generalized setting. We also show that on manifolds definable in o-minimal structures that are not polynomially bounded, such a theory can not be constructed. We present some possible applications, mainly in representation theory.
Cite
@article{arxiv.1802.01094,
title = {Tempered distributions and Schwartz functions on definable manifolds},
author = {Ary Shaviv},
journal= {arXiv preprint arXiv:1802.01094},
year = {2020}
}
Comments
In v3 the results were generalized from the sub-analytic case to the arbitrary polynomially bounded o-minimal case