English

A generalized Fourier inversion theorem

Functional Analysis 2009-03-26 v2 Operator Algebras

Abstract

In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier inversion Theorem for strictly-unconditionally integrable Fourier transforms. Our results generalize and improve those previously obtained by Ruy Exel in the case of Abelian groups.

Keywords

Cite

@article{arxiv.0802.0382,
  title  = {A generalized Fourier inversion theorem},
  author = {Alcides Buss},
  journal= {arXiv preprint arXiv:0802.0382},
  year   = {2009}
}

Comments

15 pages; some typos corrected

R2 v1 2026-06-21T10:09:15.796Z