English

Group Riesz and Frame Sequences: The Bracket and the Gramian

Functional Analysis 2016-08-10 v1

Abstract

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

Keywords

Cite

@article{arxiv.1608.02767,
  title  = {Group Riesz and Frame Sequences: The Bracket and the Gramian},
  author = {Davide Barbieri and Eugenio Hernandez and Victoria Paternostro},
  journal= {arXiv preprint arXiv:1608.02767},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1506.08942

R2 v1 2026-06-22T15:15:46.101Z