Extension of Tight Frames in Rn

Haag, Caleb (2013) Extension of Tight Frames in Rn. [Abstract]

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Abstract

Frames are redundant sets of vectors in a Hilbert space, that have lower and upper frame bounds A and B respectively, which yield one natural representation for each vector in the space, but which have infinitely many representations for a given vector. A frame is considered tight when its lower and upper frame bounds equal each other, A=B. The problem faced is whether or not we can extend a tight frame from any Rn to Rn+1 in an algorithmic way and have the new frame retain its tightness. What we found was an affirmative, geometrically meaningful solution to this problem, so yes, we can extend a tight frame into Rn+1 and have the resulting frame still be tight.

Item Type: Abstract
Created by Student or Faculty: Student
Additional Information: 8th Annual Natural & Behavioral Sciences Undergraduate Research Symposium Program
Uncontrolled Keywords: Hilbert space, tight frame, vector
Subjects: School of Natural and Behavioral Sciences > Mathematics
NBS Symposium
School of Natural and Behavioral Sciences > Physics
Depositing User: Alejandro Marquez
Date Deposited: 09 May 2013 16:36
Last Modified: 09 May 2013 16:36
URI: http://eprints.fortlewis.edu/id/eprint/233


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