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

Bill Moran, Stephen Howard, Douglas Cochran

Research output: Chapter in Book/Report/Conference proceedingChapter

7 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 publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages49-64
Number of pages16
Edition9780817683788
DOIs
StatePublished - Jan 1 2013

Publication series

NameApplied and Numerical Harmonic Analysis
Number9780817683788
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

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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

  • Applied Mathematics

Cite this

Moran, B., Howard, S., & Cochran, D. (2013). Positive-operator-valued measures: A general setting for frames. In Applied and Numerical Harmonic Analysis (9780817683788 ed., pp. 49-64). (Applied and Numerical Harmonic Analysis; No. 9780817683788). Springer International Publishing. https://doi.org/10.1007/978-0-8176-8379-5_4