A generalized Fourier inversion theorem
arXiv:0802.0382 · doi:10.1007/s00574-008-0004-6
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.
15 pages; some typos corrected