Steven Flynn

Steven Flynn
University of Bath | UB · Department of Mathematical Sciences

Doctor of Philosophy
Research Project Grant funded by the Leverhulme Trust. RPG-2020-037: Quantum limits for sub-elliptic operators.

About

5
Publications
105
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
7
Citations
Additional affiliations
September 2014 - June 2020
University of California Santa Cruz
Position
  • PhD Student
Education
September 2014 - June 2020
University of California, Santa Cruz
Field of study
  • Mathematics

Publications

Publications (5)
Chapter
In this paper, we present recent results about the developement of a semiclassical approach in the setting of nilpotent Lie groups and nilmanifolds. We focus on two-step nilmanifolds and exhibit some properties of the weak limits of sequence of densities associated with eigenfunctions of a sub-Laplacian. We emphasize the influence of the geometry o...
Preprint
In this paper, we present recent results about the developement of a semiclassical approach in the setting of nilpotent Lie groups and nilmanifolds. We focus on two-step nilmanifolds and exhibit some properties of the weak limits of sequence of densities associated with eigenfunctions of a sub-Laplacian. We emphasize the influence of the geometry o...
Preprint
Full-text available
In this paper, we consider the semi-classical setting constructed on nilpotent graded Lie groups by means of representation theory. We analyze the effects of the pull-back by diffeomorphisms on pseudodifferential operators. We restrict to diffeomorphisms that preserve the filtration and prove that they are Pansu differentiable. We show that the pul...
Article
Full-text available
We initiate the study of X-ray tomography on sub-Riemannian manifolds, for which the Heisenberg group exhibits the simplest nontrivial example. With the language of the group Fourier transform, we prove an operator-valued incarnation of the Fourier Slice Theorem, and apply this new tool to show that a sufficiently regular function on the Heisenberg...
Preprint
Full-text available
We initiate the study of X-ray tomography on sub-Riemannian manifolds, for which the Heisenberg group exhibits the simplest nontrivial example. With the language of the group Fourier Transform, we prove a operator-valued incarnation of the Fourier Slice Theorem, and apply this new tool to show that a sufficiently regular function on the Heisenberg...

Network

Cited By