Density in L2(Γ, μ) of Certain Families of Functions on LCA Groups Related to the Multi-Channel Sampling Problem. (10th August 2020)

• Record Type: Journal Article
• Authors: Klotz, Lutz P.; Medina, Juan M.
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 13(2020)
• Page Start: 1642
• Page End: 1665
• Publication Date: 2020-08-10
• Subjects: LCA groups -- sampling -- stationary random processes -- approximation theory; Primary: 42A65 -- 42C15 -- 42A10 -- Secondary: 94A20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1798996
• Languages: English
• ISSNs: 0163-0563

Abstract

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.