Translation generated oblique dual frames on locally compact groups (Q6546566)

This paper provides an illuminating unification of a variety of results concerning dual frames in the context of a second countable locally compact group \(\mathcal{G}\) with a distinguished closed abelian subgroup \(\Gamma\). This is done by studying the following general situation: Let \(\mathcal{H}\) be a separable Hilbert space and \((X,\mu_X)\) a \(\sigma\)-finite measure space such that \(L^2(X)\) is separable. The focus is on subsets and subspaces of \(L^2(X,\mathcal{H})\) and relating these to the pointwise almost everywhere corresponding subsets and subspaces of \(\mathcal{H}\). The results obtained in this general situation are then applied back in the group setting.