INVESTIGADORES
MOLTER ursula Maria
artículos
Título:
The structure of group preserving operators
Autor/es:
BARBIERI, D.; CABRELLI, C.; CARBAJAL, D.; HERNÁNDEZ, E.; MOLTER, U.
Revista:
Sampling Theory, Signal Processing, and Data Analysis
Editorial:
Birkhauser
Referencias:
Lugar: Zurich; Año: 2021 vol. 19
ISSN:
2730-5716
Resumen:
In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of L2(S) where S 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 S 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 S is the Euclidean space.