Density in L2(Γ, μ) of Certain Families of Functions on LCA Groups Related to the Multi-Channel Sampling Problem. (10th August 2020) - Klotz, Lutz P.; Medina, Juan M.
Abstract: Let G be an LCA group, H a closed subgroup, Γ the dual group of G and μ be a regular finite non-negative Borel measure on Γ. Motivated by the problem of sampling and reconstruction of a stationary random process over G from the values of m different linear measurements on H, we give some necessary or sufficient conditions for the density of certain sets of functions in L 2 ( Γ, μ ), which arise in multichannel sampling. Extensions of these results to L p ( Γ, μ ), p ≠ 2, and the existence of unconditional convergent expansions are discussed.