Finite Frames and Graph Theoretic Uncertainty Principles
Finite Frames and Graph Theoretic Uncertainty Principles
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Date
2015
Authors
Koprowski, Paul J.
Advisor
Benedetto, John J
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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.