We generalize Wiener's inversion theorem for Fourier transforms on closed subsets of the dual group of a locally compact abelian group to cosets of ideals in a class of non-commutative *-algebras having specified properties, which are all fulfilled in the case of the group algebra of any locally compact abelian group.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm137-1-7,
author = {Tobias Blendek},
title = {Wiener's inversion theorem for a certain class of *-algebras},
journal = {Colloquium Mathematicae},
volume = {135},
year = {2014},
pages = {103-116},
zbl = {1326.46042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm137-1-7}
}
Tobias Blendek. Wiener's inversion theorem for a certain class of *-algebras. Colloquium Mathematicae, Tome 135 (2014) pp. 103-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm137-1-7/