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 | Excursions in Harmonic Analysis |
| Subtitle of host publication | The February Fourier Talks at the Norbert Wiener Center |
| Publisher | Birkhauser Boston |
| Pages | 49-64 |
| Number of pages | 16 |
| Volume | 2 |
| ISBN (Electronic) | 9780817683795 |
| ISBN (Print) | 9780817683788 |
| DOIs | |
| State | Published - Jan 1 2013 |
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
- Mathematics(all)