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


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
Number of pages16
StatePublished - Jan 1 2013

Publication series

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


  • 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

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