Injectivity of the Heisenberg X-ray transform

DOI10.1016/j.jfa.2020.108886zbMath1458.53040arXiv2004.14348OpenAlexW3110933642MaRDI QIDQ826483

Steven Flynn

Publication date: 4 January 2021

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.14348

zbMATH Keywords

Heisenberg groupinverse problemsFourier slice theoremsub-Riemannian geodesicsX-ray transforms with conjugate points

Mathematics Subject Classification ID

Radon transform (44A12) Sub-Riemannian geometry (53C17)

Related Items (1)

Determination of compactly supported functions in shift-invariant space by single-angle Radon samples

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Radon transform on the Heisenberg group and the transversal Radon transform
• On Carnot-Caratheodory metrics
• L\({}^ p\) harmonic analysis and Radon transforms on the Heisenberg group
• Invariant differential operators and the range of the matrix Radon transform
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Incomplete data problems in x-ray computerized tomography
• Sub-Riemannian geometry
• Integral geometry on Grassmann manifolds and calculus of invariant differential operators
• Fourier analysis on the Heisenberg group. I. Schwartz space
• Geodesic flows
• Harmonic analysis on the Heisenberg group
• Inverting Radon transforms: the group-theoretic approach.
• A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and first Dirichlet eigenvalue of hypoelliptic operators
• Tempered distributions and Fourier transform on the Heisenberg group
• On Radon transforms on tori
• The geodesic ray transform on Riemannian surfaces with conjugate points
• Semi-classical analysis on H-type groups
• The Mathematics of Computerized Tomography
• On Radon transforms on compact Lie groups
• Phase-space analysis and pseudodifferential calculus on the Heisenberg group
• A Course in Abstract Harmonic Analysis
• The wave equation on the heisenberg group
• Integral Geometry and Radon Transforms
• On the Funk transform on compact symmetric spaces
• Noncommutative microlocal analysis. I
• On a Hilbert space of analytic functions and an associated integral transform part I
• 4. Integral geometry on manifolds with boundary and applications
• Harmonic Analysis in Phase Space. (AM-122)
• Fourier analysis on the Heisenberg group
• Reconstruction formulas for X-ray transforms in negative curvature
• The attenuated geodesic x-ray transform
• The X-ray transform on 2-step nilpotent Lie groups of higher rank
• Functional Relations, Sharp Mapping Properties, and Regularization of the X-Ray Transform on Disks of Constant Curvature
• Unitarization and Inversion Formulae for the Radon Transform Between Dual Pairs

This page was built for publication: Injectivity of the Heisenberg X-ray transform