Density in L2(µ) of certain families of functions on LCA groups related to the Multi-Channel sampling problem.

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 measureonΓ. 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 inL2(µ), which arise in multichannel sampling. Extensions of these results toLp(µ) , p≠ 2, and the existence of unconditional convergent expansions are discussed.