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.
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Acknowledgements
The authors are grateful to Somantika Datta and Benjamin Robinson for their helpful remarks on earlier drafts of this chapter.
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Moran, B., Howard, S., Cochran, D. (2013). Positive-Operator-Valued Measures: A General Setting for Frames. In: Andrews, T., Balan, R., Benedetto, J., Czaja, W., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 2. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8379-5_4
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