On an isomorphism theorem for the Feichtinger's Segal algebra on locally compact groups

Lakshmi Lavanya Ramamurthy

On an isomorphism theorem for the Feichtinger's Segal algebra on locally compact groups

Functional Analysis 2021-02-09 v2

Authors: Lakshmi Lavanya Ramamurthy

Abstract

In this article we observe that a locally compact group $G$ is completely determined by the algebraic properties of its Feichtinger's Segal algebra $S_0(G).$ Let $G$ and $H$ be locally compact groups. Then any linear (not necessarily continuous) bijection of $S_0(G)$ onto $S_0(H)$ which preserves the convolution and pointwise products is essentially a composition with a homeomorphic isomorphism of $H$ onto $G.$

Keywords

feichtinger's segal algebra locally compact groups isomorphism theorem convolution pointwise product

Cite

@article{arxiv.2102.00703,
  title  = {On an isomorphism theorem for the Feichtinger's Segal algebra on locally compact groups},
  author = {Lakshmi Lavanya Ramamurthy},
  journal= {arXiv preprint arXiv:2102.00703},
  year   = {2021}
}

Comments

12 pages

On an isomorphism theorem for the Feichtinger's Segal algebra on locally compact groups

Abstract

Keywords

Cite

Comments

Related papers