Spaces invariant under unitary representations of discrete groups
EntityUAM. Departamento de Matemáticas
10.1016/j.jmaa.2020.124357Journal of Mathematical Analysis and Applications 492.1 (2020): 124357
Funded byThis project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 777822. In addition, D. Barbieri and E. Hernández were supported by Grant MTM2016-76566-P (Ministerio de Economía y Competitividad, Spain), and V. Paternostro was supported by Grants UBACyT 20020170200057BA, CONICET-PIP 11220150100355, MINCyT-PICT 2014-1480 and 2016-2616 (Joven)
SubjectsFrames; Group representations; Invariant subspaces; Matemáticas
Rights© 2020 Elsevier Inc.
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an isometry intertwining the representation with the right regular representation, that we call a Helson map. We then characterize invariant subspaces using a Helson map, and provide general characterizations of Riesz and frame sequences of orbits. These results extend to the nonabelian setting several known results for abelian groups. They also extend to countable families of generators previous results obtained for principal subspaces
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