2019/12/28 by Carlos Cabrelli, Cabrelli, C., Carolina A. Mosquera +3
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1912.12478
openalex publication_date 2019/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given discrete groups Γ⊂ Δ we characterize (Γ,σ)-invariant spaces that are also invariant under Δ. This will be done in terms of subspaces that we define using an appropriate Zak transform and a particular partition of the underlying group. On the way, we obtain a new characterization of principal (Γ,σ)-invariant spaces in terms of the Zak transform of its generator. This result is in the spirit of the analogous in the context of shift-invariant spaces in terms of the Fourier transform, which is very well-known. As a consequence of our results, we give a solution for the problem of finding the (Γ,σ)-invariant space nearest - in the sense of least squares - to a given set of data.