Frames and Homogeneous Spaces

Let g be a locally compact non-abelian group and h be a compact subgroup of g also let μ be a g- invariant measure on the homogeneous space g/h . in this article, we extend the linear operator th: cc(g) rightarrow cc(g/h) as a bounded surjective linear operator for all lp-spaces with p geq 1 . as an application of this extension, we show that each frame for l2(g) determines a frame for l2(g/h,μ ) and each frame for l2(g/h,μ ) arises from a frame in l2(g) via the linear operator th