Range conditions for a spherical mean transform and global extendibility of solutions of the Darboux equation

DOI10.1007/s11854-010-0033-0zbMath1226.44001OpenAlexW2592605343MaRDI QIDQ628374

Nguyen Linh Viet, Mark L. Agranovsky

Publication date: 10 March 2011

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-010-0033-0

zbMATH Keywords

rangetomographyDarboux equationspherical Radon transform

Mathematics Subject Classification ID

Radon transform (44A12)

Related Items (6)

Range description for a spherical mean transform on spaces of constant curvature ⋮ Mathematics of Hybrid Imaging: A Brief Review ⋮ A Radon-type transform arising in photoacoustic tomography with circular detectors: spherical geometry ⋮ To local reconstruction from the spherical mean Radon transform ⋮ Orthogonal function series formulas for inversion of the spherical Radon transform ⋮ To recovering the moments from the spherical mean Radon transform

Cites Work

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• Mathematics of thermoacoustic tomography
• Spherical means in annular regions
• Determining a Function from Its Mean Values Over a Family of Spheres
• Inversion of Spherical Means and the Wave Equation in Even Dimensions
• The spherical mean value operator with centers on a sphere
• The range of the spherical mean value operator for functions supported in a ball

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