# Finite Frames and Graph Theoretic Uncertainty Principles

 dc.contributor.advisor Benedetto, John J en_US dc.contributor.author Koprowski, Paul J. en_US dc.date.accessioned 2015-06-26T05:44:20Z dc.date.available 2015-06-26T05:44:20Z dc.date.issued 2015 en_US dc.identifier https://doi.org/10.13016/M2ZP7W dc.identifier.uri http://hdl.handle.net/1903/16666 dc.description.abstract The subject of analytical uncertainty principles is an important field within harmonic analysis, quantum physics, and electrical engineering. We explore uncertainty principles in the context of the graph Fourier transform, and we prove additive results analogous to the multiplicative version of the classical uncertainty principle. We establish additive uncertainty principles for finite Parseval frames. Lastly, we examine the feasibility region of simultaneous values of the norms of a graph differential operator acting on a function $f\in l^2(G)$ and its graph Fourier transform. en_US dc.language.iso en en_US dc.title Finite Frames and Graph Theoretic Uncertainty Principles en_US dc.type Dissertation en_US dc.contributor.publisher Digital Repository at the University of Maryland en_US dc.contributor.publisher University of Maryland (College Park, Md.) en_US dc.contributor.department Mathematics en_US dc.subject.pqcontrolled Mathematics en_US
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