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You searched for id:"oai:tigerprints.clemson.edu:all_dissertations-3641". One record found.

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Clemson University

1. Green, Andrew Walton. The Uncertainty Principle in Control Theory for Partial Differential Equations.

Degree: PhD, Mathematical Sciences, 2020, Clemson University

In this thesis, we will study the interaction between problems in control theory for partial differential equations and inequalities of the uncertainty principle type. The main results will concern the boundary observability of the viscoelastic wave equation and energy decay rates of damped wave equations. In the boundary case, we will prove what may be viewed as a higher dimensional version of Ingham's inequality, replacing the complex exponentials with Laplacian eigenfunctions. For energy decay rates on the real line, we will use a version of the Paneah-Logvinenko-Sereda theorem for functions with Fourier support contained in multiple intervals. We prove the exact variation which we need and apply it to internal observability as well as decay rates for damped wave equations as well. We also give partial results in higher dimensions and some open problems. We will also investigate the connection between compactness of localization operators and uncertainty principles from an abstract harmonic analysis perspective. We give some general results which are applied to the wavelet transform. Advisors/Committee Members: Mishko Mitkovski, Benjamin Jaye, Jeong-Rock Yoon.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Green, A. W. (2020). The Uncertainty Principle in Control Theory for Partial Differential Equations. (Doctoral Dissertation). Clemson University. Retrieved from https://tigerprints.clemson.edu/all_dissertations/2636

Chicago Manual of Style (16th Edition):

Green, Andrew Walton. “The Uncertainty Principle in Control Theory for Partial Differential Equations.” 2020. Doctoral Dissertation, Clemson University. Accessed July 08, 2020. https://tigerprints.clemson.edu/all_dissertations/2636.

MLA Handbook (7th Edition):

Green, Andrew Walton. “The Uncertainty Principle in Control Theory for Partial Differential Equations.” 2020. Web. 08 Jul 2020.

Vancouver:

Green AW. The Uncertainty Principle in Control Theory for Partial Differential Equations. [Internet] [Doctoral dissertation]. Clemson University; 2020. [cited 2020 Jul 08]. Available from: https://tigerprints.clemson.edu/all_dissertations/2636.

Council of Science Editors:

Green AW. The Uncertainty Principle in Control Theory for Partial Differential Equations. [Doctoral Dissertation]. Clemson University; 2020. Available from: https://tigerprints.clemson.edu/all_dissertations/2636

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