Title of dissertation : Finite Frames and Graph Theoretical Uncertainty Principles Paul
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چکیده
Title of dissertation: Finite Frames and Graph Theoretical Uncertainty Principles Paul J. Koprowski, Doctor of Philosophy, 2015 Dissertation directed by: Dr. John J. Benedetto Department of Mathematics 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 ∈ l(G) and its graph Fourier transform. Finite Frames and Graph Theoretic Uncertainty Principles by Paul J. Koprowski Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2015 Advisory Committee: Dr. John J. Benedetto, Chair/Advisor Dr. Kenneth Berg, Dr. Wojciech Czaja, Dr. Patrick M. Fitzpatrick, Dr. Kasso A. Okoudjou Dr. Kaye Brubaker, Dean’s Representative c © Copyright by Paul J. Koprowski 2015
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