Le problème de Pompeiu local. (Local Pompeiu problem)

DOI10.1007/BF02820476zbMath0668.30037MaRDI QIDQ1118069

Roger Gay, Carlos. A. Berenstein

Publication date: 1989

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

zbMATH Keywords

Gauss theoremPompeiu transformMorera Theorem

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Miscellaneous topics in partial differential equations (35R99) Miscellaneous topics of analysis in the complex plane (30E99) Integral transforms, operational calculus (44A99)

Related Items (11)

Injectivity of the Pompeiu transform in the Heisenberg group ⋮ Morera and mean-value type theorems in the hyperbolic disk ⋮ Extremal cases of the Pompeiu problem. ⋮ Analogs of Stokes's formula for polyhedra ⋮ Morera theorems via microlocal analysis ⋮ Infinite systems of convolution equations on multidimensional domains ⋮ Sets with the Pompeiu property on the plane and on the sphere ⋮ Convolution equations and the local Pompeiu property on symmetric spaces and on phase space associated to the Heisenberg group ⋮ Inversion of the local Pompeiu transform ⋮ Morera theorems for complex manifolds ⋮ Pompeiu transforms on geodesic spheres in real analytic manifolds

Cites Work

• A local version of the two-circles theorem
• Pompeiu's problem on symmetric spaces
• Analyticity and the Pompeiu problem
• Spectral synthesis and the Pompeiu problem
• A Radon Transform on Spheres Through the Origin in R n and Applications to the Darboux Equation
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