English

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.

Keywords

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

R2 v1 2026-06-21T19:31:44.853Z