Spectral synthesis in $L^2(G)$
Volume 138 / 2015
Colloquium Mathematicum 138 (2015), 89-103
MSC: Primary 43A45, 43A85; Secondary 22E30.
DOI: 10.4064/cm138-1-6
Abstract
For locally compact, second countable, type I groups $G$, we characterize all closed (two-sided) translation invariant subspaces of $L^2(G)$. We establish a similar result for $K$-biinvariant $L^2$-functions ($K$ a fixed maximal compact subgroup) in the context of semisimple Lie groups.
