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Title:Projections, slicings and Fourier transforms in the Heisenberg group
Author(s):Roman-Garcia, Fernando Yahdiel
Director of Research:Tyson, Jeremy T
Doctoral Committee Chair(s):Junge, Marius
Doctoral Committee Member(s):Erdogan, Mehmet B; Kaufman, Robert P
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Heisenberg group, Hausdorff dimension, projections, Fourier transform.
Abstract:This thesis starts by giving an expository introduction to the study of projection and slicing problems in the Heisenberg group from the point of view of Hausdorff dimension distortion. It then gives a short summary of research done in this area up to date before introducing and explaining my own contributions to it. Finally, the group Fourier transform in the Heisenberg group is introduced and a novel connection with Hausdorff dimension is discussed.
Issue Date:2020-05-01
Type:Thesis
URI:http://hdl.handle.net/2142/107941
Rights Information:Copyright 2020 Fernando Roman-Garcia
Date Available in IDEALS:2020-08-26
Date Deposited:2020-05


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