Schwartz functions, tempered distributions, and Kernel Theorem on solvable Lie groups
Functional Analysis
2010-02-11 v1 Group Theory
Abstract
Let G be a solvable Lie group endowed with right Haar measure. We define and study a dense Frechet *-subalgebra S of L1(G), consisting of smooth functions rapidly-decreasing at infinity on G. When G is nilpotent, we recover the classical Schwartz algebra introduced by R. Howe and other authors. We develop a distribution theory for S, and we generalize the classical Kernel Theorem of L. Schwartz to our setting.
Keywords
Cite
@article{arxiv.1002.2185,
title = {Schwartz functions, tempered distributions, and Kernel Theorem on solvable Lie groups},
author = {E. David-Guillou},
journal= {arXiv preprint arXiv:1002.2185},
year = {2010}
}
Comments
36 pages