Group Riesz and frame sequences: the Bracket and the Gramian

• Autores: Davide Barbieri, Eugenio Hernández Rodríguez , Victoria Paternostro
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 69, Fasc. 2, 2018, págs. 221-236
• Idioma: inglés
• DOI: 10.1007/s13348-017-0202-x
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• Resumen

  • Given a discrete group and a unitary representation on a Hilbert space , we prove that the notions of operator Bracket map and Gramian coincide on a dense set of . As a consequence, combining this result with known frame theory, we can recover all previous Bracket characterizations of Riesz and frame sequences generated by a single element under a unitary representation.