Inversion Formulas for the Spherical Means in Constant Curvature Spaces

Keywords

Constant curvature, Integral geometry, Hyperbolic space, Mathematics, Geodesic

References

• Integral Geometry and Radon TransformsSigurđur Helgason — 2010
• Selected Topics in Integral GeometryI. M. Gel'fand, Simon Gindikin, М. И. Граев — 2003
• Singular and degenerate Cauchy problemsR. Carroll, R. Showalter — 1976
• The Universality of the Radon TransformLeon Ehrenpreis — 2003
• THE GENERALIZED MADER'S INVERSION FORMULAS FOR THE RADON TRANSFORMSY. A. Antipov, Boris Rubin — 2011
• Fractional Integrals and PotentialsBoris Rubin — 1996
• Plane Waves and Spherical Means: Applied To Partial Differential EquationsFritz John — 1981
• Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory IntegralsElias M. Stein, Timothy S Murphy — 1993
• Review: E. C. Titchmarsh, Introduction to the Theory of Fourier IntegralsJ. D. Tamarkin — 1938
• Coxeter system of lines are sets of injectivity for the twisted spherical means on CR. K. Srivastava — 2011
• The range of the spherical mean value operator for functions supported in a ballDavid Finch, Rakesh Rakesh — 2006
• Range descriptions for the spherical mean Radon transform. I. Functions supported in a ballMark Agranovsky, Peter Kuchment, Eric Todd Quinto — 2006
• Range conditions for a spherical mean transformMark Agranovsky, David Finch, Peter Kuchment — 2009
• Singular Cauchy problems in symmetric spacesRobert W. Carroll — 1976
• The spherical mean value operator with centers on a sphereDavid Finch, Rakesh Rakesh — 2007
• A Range Description for the Planar Circular Radon TransformGaik Ambartsoumian, Peter Kuchment — 2005
• Inversion of Spherical Means and the Wave Equation in Even DimensionsDavid Finch, Markus Haltmeier, Rakesh Rakesh — 2007
• Universal back-projection algorithm for photoacoustic computed tomographyMinghua Xu, Lihong V. Wang — 2005
• Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous mediaYulia Hristova, Peter Kuchment, Linh V. Nguyen — 2008
• Inversion formulae for the spherical mean in odd dimensions and the Euler–Poisson–Darboux equationBoris Rubin — 2008

Cited by

• Recovering finite parametric distributions and functions using the spherical mean transformYehonatan Salman — 2016
• Recovering Functions Defined on S^n - 1 by Integration on Subspheres Obtained from Hyperplanes Tangent to a SpheroidYehonatan Salman — 2017
• Recovering functions from the spherical mean transform with data on an ellipse using eigenfunction expansion in elliptical coordinatesYehonatan Salman — 2017
• The Spherical Mean Transform with Data on a Parabola in the PlaneYehonatan Salman — 2018
• Reconstruction of Radar Images by Using Spherical Mean and Regular Radon TransformsOzan Pirbudak — 2019
• Spherical Sliced-WassersteinClément Bonet, Paul Berg, Nicolas Courty — 2022

Related papers

• The Inversion of Ray Transforms on a Conformal Class of CurvesNicholas Hoell, Guillaume Bal — 2010
• Dual area measures and local additive kinematic formulasAndreas Bernig — 2017
• Applications of a distance formula in hyperbolic plane geometryDavid E. Dobbs — 2001
• C∞ smooth freeform surfaces over hyperbolic domainsWei Zeng, Ying He, Jiazhi Xia — 2009
• Inverse spectral problems on hyperbolic manifolds and their applications to inverse boundary value problems in Euclidean spaceHiroshi Isozaki — 2004
• On the geometric origin of the equation ϕ,11 — ϕ,22 = eϕ — e-2ϕV. V. Nesterenko — 1980
• The Inversion of Ray Transforms on a Conformal Class of CurvesNicholas Hoell, Guillaume Bal — 2010
• Slow invariant manifolds as curvature of the flow of dynamical systemsJean‐Marc Ginoux, Bruno Rossetto, Leon O. Chua — 2015
• A new approach to some nonlinear geometric equations in dimension twoFengbo Hang, Xiaodong Wang — 2006
• On Restricting Planar Curve Evolution to Finite Dimensional Implicit Subspaces with Non-Euclidean MetricAditya Tatu, François Lauze, Stefan Sommer — 2010