Mathematics – Functional Analysis
Scientific paper
2009-10-30
Mathematics
Functional Analysis
19 pages, LateX with AMS macros; corrections addressing complications due to zero vectors and spark
Scientific paper
The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy for finite frames in a Hilbert space. This motivates a carefully chosen list of desired properties for upper and lower redundancies. The means to achieve these properties is to consider the maximum and minimum of a redundancy function, which is interesting in itself. The redundancy function is defined on the sphere of the Hilbert space and measures the concentration of frame vectors around each point. A complete characterization of functions on the sphere which coincide with a redundancy function for some frame is given. The upper and lower redundancies obtained from this function are shown to satisfy all of the intuitively desirable properties. In addition, the range of values they assume is characterized.
Bodmann Bernhard G.
Casazza Peter G.
Kutyniok Gitta
No associations
LandOfFree
A quantitative notion of redundancy for finite frames does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A quantitative notion of redundancy for finite frames, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A quantitative notion of redundancy for finite frames will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-90207