info:eu-repo/semantics/article
The structure of group preserving operators
Fecha
2021-04-27Registro en:
Barbieri, Davide; Cabrelli, Carlos; Carbajal, Diana Agustina; Hernández Rodríguez, Eugenio; Molter, Ursula Maria; The structure of group preserving operators; Springer; Sampling Theory, Signal Processing, and Data Analysis; 19; 1; 27-4-2021; 1-22
2730-5716
2730-5724
CONICET Digital
CONICET
Autor
Barbieri, Davide
Cabrelli, Carlos
Carbajal, Diana Agustina
Hernández Rodríguez, Eugenio
Molter, Ursula Maria
Resumen
In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of 2() where is a second countable LCA group. The subspaces where the operators act are invariant under the action of a group Γ which is a semi-direct product of a uniform lattice of with a discrete group of automorphisms. This class includes the crystal groups which are important in applications as models for images. The operators are assumed to be Γ preserving. i.e. they commute with the action of Γ. In particular, we obtain a spectral decomposition for these operators. This generalizes recent results on shift-preserving operators acting on lattice invariant subspaces where is the Euclidean space.