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Operator-Valued Frames Associated with Measure Spaces


Abstract Since Duffin and Schaeffer's introduction of frames in 1952, the concept of a frame has received much attention in the mathematical community and has inspired several generalizations. The focus of this thesis is on the concept of an operator-valued frame (OVF) and a more general concept called herein an operator-valued frame associated with a measure space (MS-OVF), which is sometimes called a continuous g-frame. The first of two main topics explored in this thesis is the relationship between MS-OVFs and objects prominent in quantum information theory called positive operator-valued measures (POVMs). It has been observed that every MS-OVF gives rise to a POVM with invertible total variation in a natural way. The first main result of thi... (more)
Created Date 2014
Contributor Robinson, Benjamin David (Author) / Cochran, Douglas (Advisor) / Moran, William (Advisor) / Boggess, Albert (Committee member) / Milner, Fabio (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Subject Mathematics / Frames / G-frames / Operator-valued frames / Radon-Nikodym theorems / Representation theory / Sampling
Type Doctoral Dissertation
Extent 87 pages
Language English
Copyright
Reuse Permissions All Rights Reserved
Note Doctoral Dissertation Mathematics 2014
Collaborating Institutions Graduate College / ASU Library
Additional Formats MODS / OAI Dublin Core / RIS


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Description Dissertation/Thesis