Extra-invariance of group actions

C. CABRELLI; C. MOSQUERA; V. PATERNOSTRO

THE JOURNAL OF GEOMETRIC ANALYSIS

SPRINGER

Lugar: Berlin; Año: 2021 vol. 31 p. 11878 - 11898

1050-6926

Given discrete groups Γ ⊂ ∆ we characterize (Γ, σ)-invariant spaces that are also invariant under ∆. 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 well-known characterization of shift-invariant spaces in terms of the Fourier transform. 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