Positive-operator-valued measures: A general setting for frames

Bill Moran, Stephen Howard, Douglas Cochran

Research output: Chapter in Book/Report/Conference proceedingChapter

8 Scopus citations

Abstract

This chapter presents an overview of close parallels that exist between the theory of positive-operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important generalizations. The concept of a framed POVM is introduced, and classical frames, fusion frames, generalized frames, and other variants of frames are all shown to arise as framed POVMs. This observation allows drawing on a rich existing theory of POVMs to provide new perspectives in the study of frames.

Original languageEnglish (US)
Title of host publicationExcursions in Harmonic Analysis
Subtitle of host publicationThe February Fourier Talks at the Norbert Wiener Center
PublisherBirkhauser Boston
Pages49-64
Number of pages16
Volume2
ISBN (Electronic)9780817683795
ISBN (Print)9780817683788
DOIs
StatePublished - Jan 1 2013

Keywords

  • Frame
  • Framed POVM
  • Fusion frame
  • Generalized frame
  • Naimark's theorem
  • Positive operator-valued measure(POVM)
  • Radon-nikodym theorem
  • Spectral measure
  • Stinespring's theorem

ASJC Scopus subject areas

  • Mathematics(all)

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