Sums of plane waves, and the range of the Radon transform

DOI10.1007/BF01420422zbMath0424.35005OpenAlexW2073804083MaRDI QIDQ1134896

Bent E. Petersen, Kennan T. Smith, Donald C. Solmon

Publication date: 1979

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/182810

zbMATH Keywords

Sobolev spacesRadon transformssums of plane waves

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Wave equation (35L05) Transform methods (e.g., integral transforms) applied to PDEs (35A22)

Related Items (5)

On the closedness of the sum of ranges of operators \(A_k\) with almost compact products \(A_i^\ast A_j\) ⋮ On sums of subspaces in topological vector spaces and an application in theoretical tomography ⋮ Sums of homogeneous functions and the range of the divergent beam x-ray transform ⋮ Smoothness and uniqueness in ridge function representation ⋮ On the closure of spaces of sums of Ridge functions and the range of the X-ray transform

Cites Work

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• The angles between the null spaces of X rays
• Optimal reconstruction of a function from its projections
• Theory of Bessel potentials. II
• Practical and mathematical aspects of the problem of reconstructing objects from radiographs
• Consistency conditions for a finite set of projections of a function

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