Pompeiu transforms on geodesic spheres in real analytic manifolds

DOI10.1007/BF02760947zbMath0791.58017MaRDI QIDQ1310420

Eric Todd Quinto

Publication date: 3 January 1994

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

geodesic spheresincidence relationPompeiu transforms

Mathematics Subject Classification ID

Integration on manifolds; measures on manifolds (58C35) Differential geometry of symmetric spaces (53C35) Harmonic analysis and spherical functions (43A90) Real-analytic manifolds, real-analytic spaces (32C05)

Related Items (11)

On the strength of streak artifacts in filtered back-projection reconstructions for limited angle weighted X-ray transform ⋮ Optimization problems related to the John uniqueness theorem ⋮ Inversion of the local Pompeiu transform in real and complex hyperbolic spaces: Case of two balls ⋮ The extension problem for functions with zero weighted spherical means ⋮ Morera theorems via microlocal analysis ⋮ On functions on a sphere with zero integrals over circumferences with fixed radius ⋮ Analog of the John theorem for weighted spherical means on a sphere ⋮ Two radius support theorem for the sphere transform ⋮ On functions on the sphere with zero integrals over geodesics ⋮ Morera theorems for complex manifolds ⋮ Geometry of stationary sets for the wave equation in \(\mathbb R^n\): the case of finitely supported initial data

Cites Work

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• Inversion of the local Pompeiu transform
• Moyennes généralisées
• The invertibility of rotation invariant Radon transforms
• A local version of the two-circles theorem
• Support theorems for real-analytic Radon transforms
• Le problème de Pompeiu local. (Local Pompeiu problem)
• Pompeiu's problem on symmetric spaces
• Spherical means on Riemannian manifolds
• Differential operators on homogeneous spaces
• Functions on a sphere with vanishing integrals over certain subspheres
• Analyticity and the Pompeiu problem
• Spherical Means and Geodesic Chains on a Riemannian Manifold
• Offbeat Integral Geometry
• The Dependence of the Generalized Radon Transform on Defining Measures
• Support Theorems for Radon Transforms on Real Analytic Line Complexes in Three-Space

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