Range description for a spherical mean transform on spaces of constant curvatures

2011/07/08 by Linh V. Nguyen, Nguyen, Linh V.
Engineering · Mathematics · #35R01 #53C65 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.1107.1746

openalex publication_date 2011/07/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We describe the range of a restricted spherical mean transform, which sends a function supported inside a closed ball in a hyperbolic space to its mean values on the geodesics spheres centered at the boundary of the ball. The description resembles that of the same transform on the Euclidean spaces obtained by Mark Agranovsky, David Finch, and Peter Kuchment [Inverse Problems and Imaging, 3(3):373--382, 2009] and Mark Agranovsky and Linh V. Nguyen [J. Anal. Math., 112:351--367, 2010]. We also derive a similar characterization for the corresponding transform on the two dimensional spherical space.

Citations

• The spherical mean value operator with centers on a sphere
• Range conditions for a spherical mean transform and global extendibility of solutions of the darboux equation

Related

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• Range conditions for a spherical mean transform and global extension of solutions of Darboux equation
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• The spherical mean value operator with centers on a sphere