English

Analytic Dirac approximation for real linear algebraic groups

Representation Theory 2010-02-25 v1

Abstract

For a real linear algebraic group G let A(G) be the algebra of analytic vectors for the left regular representation of G on the space of superexponentially decreasing functions. We present an explicit Dirac sequence in A(G). Since A(G) acts on E for every Frechet-representation (\pi,E) of moderate growth, this yields an elementary proof of a result of Nelson that the space of analytic vectors is dense in E.

Keywords

Cite

@article{arxiv.1002.4462,
  title  = {Analytic Dirac approximation for real linear algebraic groups},
  author = {Christoph Lienau},
  journal= {arXiv preprint arXiv:1002.4462},
  year   = {2010}
}

Comments

7 pages

R2 v1 2026-06-21T14:50:30.761Z