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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/25582

Title: Convergence Results for Rearrangements: Old and New.
Authors: Fortier, Marc
Advisor: Burchard, Almut
Department: Mathematics
Issue Date: 31-Dec-2010
Abstract: The purpose of this thesis is twofold. On the one hand, it aims to give a thorough review and exposition of current best results regarding approximating the symmetric decreasing rearrangement by polarizations and Steiner symmetrizations. These results include those of Van Schaftingen on explicit universal approximation to the symmetric decreasing rearrangement by sequences of polarizations as well as his results on almost sure convergence of rearrangements to the symmetric decreasing rearrangement. They also include those of Klartag and Milman which yield rates of convergence for Steiner symmetrizations of convex bodies. On the other hand, new results are proven. We extend Van Schaftingen's results on almost sure convergence of polarizations and Steiner symmetrizations by showing that the conditions on the random variables can be weakened without affecting almost sure convergence to the symmetric decreasing rearrangement. Lastly, we derive rates of convergence for polarizations and Steiner symmetrizations of Hölder continuous functions.
URI: http://hdl.handle.net/1807/25582
Appears in Collections:Master
Department of Mathematics - Master theses

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