Vanishing of quasi-invariant generalized functions (Q2875841)

On the Euclidean space, the dual of the space of smooth functions with compact support is the space of distributions, and the space of smooth functions can be canonically mapped injectively into the space of distributions, due to the canonical Lebesgue measure on the Euclidean space. For a noncompact smooth manifold \(M\), the dual of the space of smooth functions on \(M\) with compact support is the space of distributions. In this case, distributions are really densities, and there is also related a space of generalized functions which contains the space of smooth functions as a dense subspace. In this paper, the authors review ``some new and easy-to-use techniques to show vanishing of quasi-invariant generalized functions'', which were developed in their paper [Trans. Am. Math. Soc. 363, No. 5, 2763--2802 (2011; Zbl 1217.22011)]. The reason is that the determination of quasi-invariant generalized functions is important for several problems in representation theory such as character theory and restrictions problems.NEWLINENEWLINEFor the entire collection see [Zbl 1284.00072].