Projections, slicings and Fourier transforms in the Heisenberg group

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Roman-Garcia, Fernando Yahdiel

Contributors dc:contributor

• Tyson, Jeremy T
• Junge, Marius
• Erdogan, Mehmet B
• Kaufman, Robert P

• Heisenberg group, Hausdorff dimension, projections, Fourier transform.

Statement dc:rights

• Copyright 2020 Fernando Roman-Garcia

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/107941

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/107941