In this paper we will extend to non-abelian groups inverse spectral results, proved by us in an earlier (Guillemin and Wang, 2016), for compact abelian groups, i.e. tori. More precisely, Let G be a Lie group acting isometrically on Riemannian manifold X. We show that the Schrödinger operator ??2?+V with V?C?(X)G, potential function V is, some interesting examples, determined G-equivariant spect...

let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

A systematic analysis is made of the character of the free and free abelian topological groups on uniform spaces and on topological spaces. In the case of the free abelian topological group on a uniform space, expressions are given for the character in terms of simple cardinal invariants of the family of uniformly continuous pseudometrics of the given uniform space and of the uniformity itself....