6 papers
Quantization on filtered manifolds
Clotilde Fermanian Kammerer, Véronique Fischer, Steven Flynn
In this article, we develop a pseudodifferential calculus on a general filtered manifold M . The symbols are fields of operators (x, ) parametrised by x M and the unita…
Injectivity and stability for the sub-Riemannian X-ray transform on H-type groups
Steven Flynn
We prove injectivity and a stability estimate for the X-ray transform along sub-Riemannian geodesics of -type groups, a setting in which almost every geodesic carries conjugate…
Singular Value Decomposition for the X-ray Transforms on the Reduced Heisenberg Group, and a Two-Radius Theorem
Steven Flynn
We give an explicit Singular Value Decomposition of the sub-Riemannian X-ray transform on the Heisenberg group with compact center. By studying the singular values, we obtain a two…
Some remarks on semi-classical analysis on two-step Nilmanifolds
Clotilde Fermanian Kammerer, Véronique Fischer, Steven Flynn
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 nilmanifol…
Geometric invariance of the semi-classical calculus on nilpotent graded Lie groups
Clotilde Fermanian Kammerer, Veronique Fischer, Steven Flynn
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 diffe…
Injectivity of the Heisenberg X-ray Transform
Steven Flynn
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 Fouri…