The Resource Fusion frame constructions and frame partitions, by Jesse Peterson

Fusion frame constructions and frame partitions, by Jesse Peterson

Label
Fusion frame constructions and frame partitions
Title
Fusion frame constructions and frame partitions
Statement of responsibility
by Jesse Peterson
Creator
Contributor
Author
Thesis advisor
Subject
Genre
Language
eng
Summary
Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Despite extensive literature on fusion frames, and several construction methods for unit-weight fusion frames with prescribed subspace dimensions and fusion frame operator spectra, there do not exist such constructions for prescribed non-unit weights. There are also very few constructions which allow one to control geometric properties among the subspaces. First we will adapt a flexible construction technique known as spectral tetris to provide the first constructions of the most general classes of fusion frames: fusion frames with arbitrary non-unit weights. Moreover, we provide for the first time necessary and sufficient conditions for when a fusion frame can be constructed via spectral tetris methods. Then we present a new alternative construction leveraging Naimark complements to build a large class of fusion frames whose principal angles between any two subspaces are constant. Changing focus to frame partitions, the celebrated Rado-Horn theorem is an often-applied tool which provides a tight bound on the minimal number of linearly indpendent sets in a partition of vectors. This theorem has been rediscovered many times over, but no existing results describe how to find such partitions. We present an alternative proof of the Rado-Horn theorem and then adapt our proof's ideas to capture much more spanning and independence information compared with existing Rado-Horn results. We further describe how to build partitions with these properties
Cataloging source
MUU
http://library.link/vocab/creatorName
Peterson, Jesse D
Degree
Ph. D.
Dissertation note
Thesis
Dissertation year
2013.
Government publication
government publication of a state province territory dependency etc
Granting institution
University of Missouri--Columbia
Index
no index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • theses
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1945-
http://library.link/vocab/relatedWorkOrContributorName
Casazza, Peter G.
http://library.link/vocab/subjectName
Frames (Vector analysis)
Label
Fusion frame constructions and frame partitions, by Jesse Peterson
Instantiates
Publication
Note
  • "A Dissertation presented to the Faculty of the Graduate School at the University of Missouri In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy."
  • Dissertation Supervisor: Dr. Peter Casazza
  • Vita
Bibliography note
Includes bibliographical references (pages 75-81)
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier.
Content category
text
Content type code
txt
Content type MARC source
rdacontent.
Control code
871332084
Extent
1 online resource (vii, 82 pages).
Form of item
online
Media category
computer
Media MARC source
rdamedia.
Media type code
c
Specific material designation
remote
System control number
(OCoLC)871332084
Label
Fusion frame constructions and frame partitions, by Jesse Peterson
Publication
Note
  • "A Dissertation presented to the Faculty of the Graduate School at the University of Missouri In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy."
  • Dissertation Supervisor: Dr. Peter Casazza
  • Vita
Bibliography note
Includes bibliographical references (pages 75-81)
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier.
Content category
text
Content type code
txt
Content type MARC source
rdacontent.
Control code
871332084
Extent
1 online resource (vii, 82 pages).
Form of item
online
Media category
computer
Media MARC source
rdamedia.
Media type code
c
Specific material designation
remote
System control number
(OCoLC)871332084

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