Spaces invariant under unitary representations of discrete groups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:492

Article

Barbieri, Davide¹  Hernandez, Eugenio¹  Paternostro, Victoria^2,3 

[1] Univ Autonoma Madrid, Madrid 28049, Spain

[2] Univ Buenos Aires, RA-1428 Buenos Aires, DF, Argentina

[3] Consejo Nacl Invest Cient & Tecn, IMAS CONICET, RA-1428 Buenos Aires, DF, Argentina

关键词: Frames;    Group representations;    Invariant subspaces;   

DOI  :  10.1016/j.jmaa.2020.124357

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free