We introduce quantum tomography on locally compact Abelian groups $G$. A linear map from the set of states $C^*$-algebra $A(G)$ generated by projective unitary representation $G$ to space characteristic functions is constructed. The dual determining symbols observables derived. Given a function state tomogram consisting probability distributions introduced. provide three examples in which $G={\...

A locally compact topological group G is called an (H) group if G has a maximal compact normal subgroup with Lie factor. In this note, we study the problem when a locally compact group is an (H) group. Let G be a locally compact Hausdorff topological group. Let G0 be the identity component of G. If G/G0 is compact, then we say that G is almost connected. The structure of almost connected locall...