@inbook{9f61c051b6be44a9a7ebd1a7842c13d9,
title = "Positive-operator-valued measures: A general setting for frames",
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.",
keywords = "Frame, Framed POVM, Fusion frame, Generalized frame, Naimark{\textquoteright}s Theorem, Positive operator-valued measure(POVM), Radon-Nikodym Theorem, Spectral measure, Stinespring{\textquoteright}s Theorem",
author = "Bill Moran and Stephen Howard and Douglas Cochran",
year = "2013",
month = jan,
day = "1",
doi = "10.1007/978-0-8176-8379-5_4",
language = "English (US)",
series = "Applied and Numerical Harmonic Analysis",
publisher = "Springer International Publishing",
number = "9780817683788",
pages = "49--64",
booktitle = "Applied and Numerical Harmonic Analysis",
edition = "9780817683788",
}