Operator-Valued Frames for the Heisenberg Group

Benjamin Robinson, William Moran, Douglas Cochran, Stephen D. Howard

Research output: Contribution to journalArticlepeer-review

Abstract

A classical result of Duffin and Schaeffer gives conditions under which a discrete collection of characters on forms a Hilbert-space frame for For the case of characters with period one, this is just the Poisson Summation Formula. Duffin and Schaeffer show that perturbations preserve the frame condition in this case. This paper gives analogous results for the real Heisenberg group where frames are replaced by operator-valued frames. The Selberg Trace Formula is used to show that perturbations of the orthogonal case continue to behave as operator-valued frames. This technique enables the construction of decompositions of elements of for suitable subsets $$E$$E of $$H_n$$Hn in terms of representations of

Original languageEnglish (US)
Pages (from-to)1384-1397
Number of pages14
JournalJournal of Fourier Analysis and Applications
Volume21
Issue number6
DOIs
StatePublished - May 6 2015

Keywords

  • G-frames
  • Heisenberg Group
  • Operator-valued frames
  • Representations
  • Sampling

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

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