Projections, slicings and Fourier transforms in the Heisenberg group

Heisenberg group, Hausdorff dimension, projections, Fourier transform.

Roman-Garcia, Fernando Yahdiel

关键词: Heisenberg group, Hausdorff dimension, projections, Fourier transform.;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/107941/ROMAN-GARCIA-DISSERTATION-2020.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.