We consider various generalizations of linear homogeneous distributions on adeles and construct a number of algebras of non-linear generalized functions on adeles and totally disconnected groups such as the discrete adeles.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-19, author = {Yakov V. Radyno and Yauhen M. Radyna}, title = {Generalized functions on adeles. Linear and non-linear theories}, journal = {Banach Center Publications}, volume = {89}, year = {2010}, pages = {243-250}, zbl = {1195.43003}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-19} }
Yakov V. Radyno; Yauhen M. Radyna. Generalized functions on adeles. Linear and non-linear theories. Banach Center Publications, Tome 89 (2010) pp. 243-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-19/