Positive Operator Valued Measures: A General Setting for Frames
Functional Analysis
2011-11-08 v1 Classical Analysis and ODEs
Abstract
This paper 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 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.
Cite
@article{arxiv.1111.1450,
title = {Positive Operator Valued Measures: A General Setting for Frames},
author = {Bill Moran and Stephen Howard and Doug Cochran},
journal= {arXiv preprint arXiv:1111.1450},
year = {2011}
}
Comments
17 pages; Prepeared for Proceedings of the February Fourier Talks