Abstract
Wiener has shown that an integrable function on the circle T which is square integrable near the identity and has nonnegative Fourier transform, is square integrable on all of T. In the last 30 years this has been extended by the work of various authors step by step. The latest result states that, in a suitable reformulation, Wiener's theorem with ``p-integrable'' in place of ``square integrable'' holds for all even p and fails for all other p (1, ∞) in the case of a general locally compact abelian group. We extend this to all IN-groups (locally compact groups with at least one invariant compact neighbourhood) and show that an extension to all locally compact groups is not possible: Wiener's theorem fails for all p < ∞ in the case of the ax + b-group.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
