Continuity of the Radon transform and its inverse on Euclidean space

DOI10.1007/BF01252856zbMath0507.46036OpenAlexW2074682845MaRDI QIDQ1837373

Alexander Hertle

Publication date: 1983

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

Full work available at URL: https://eudml.org/doc/173356

zbMATH Keywords

Radon transformFourier integral operatorlocal singularitymaximal extensionapriori analyticityinverse continuityRadon-Borel isomorphismspace integrable distributions

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Pseudodifferential and Fourier integral operators on manifolds (58J40) Integral equations with miscellaneous special kernels (45H05)

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Cites Work

• Unnamed Item
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• The Radon transform
• \(L^ p\) estimates for Radon transforms in Euclidean and non-Euclidean spaces
• The Radon transform on Zoll surfaces
• The surjectivity of invariant differential operators on symmetric spaces. I
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• Abhängigkeiten zwischen den Flächenintegralen einer stetigen Funktion
• Practical and mathematical aspects of the problem of reconstructing objects from radiographs
• A Characterization of Fourier and Radon Transforms on Euclidean Space
• A Sobolev Space Analysis of Picture Reconstruction
• Picture reconstruction from projections in restricted range
• The Dependence of the Generalized Radon Transform on Defining Measures
• The finite element method for ill-posed problems
• Uniform asymptotic expansions at a caustic
• Produits tensoriels topologiques et espaces nucléaires

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