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

Bill Moran; Stephen Howard; Douglas Cochran

doi:10.1007/978-0-8176-8379-5_4

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

Bill Moran, Stephen Howard, Douglas Cochran

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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 language	English (US)
Title of host publication	Applied and Numerical Harmonic Analysis
Publisher	Springer International Publishing
Pages	49-64
Number of pages	16
Edition	9780817683788
DOIs	https://doi.org/10.1007/978-0-8176-8379-5_4
State	Published - Jan 1 2013

Publication series

Name	Applied and Numerical Harmonic Analysis
Number	9780817683788
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

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Access to Document

10.1007/978-0-8176-8379-5_4