Spaces invariant under unitary representations of discrete groups
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 reg...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2020 |
| País: | España |
| Recursos: | Universidad Autónoma de Madrid |
| Repositório: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.uam.es:10486/700632 |
| Acesso em linha: | http://hdl.handle.net/10486/700632 https://dx.doi.org/10.1016/j.jmaa.2020.124357 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Frames Group representations Invariant subspaces Matemáticas |
| Resumo: | 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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