Schwartz functions, tempered distributions, and Kernel Theorem on solvable Lie groups

Details Schwartz functions, tempered distributions, and Kernel Theorem on solvable Lie groups Schwartz functions, tempered distributions, and Kernel Theorem on solvable Lie groups

2010-02-10

arxiv.org/abs/1002.2185v1

Mathematics

Functional Analysis

36 pages

Scientific paper

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.

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