Inversion of the local Pompeiu transform in real and complex hyperbolic spaces: Case of two balls

DOI10.1007/BF02787785zbMath0865.32021MaRDI QIDQ1911483

Mimoun El Harchaoui

Publication date: 7 July 1997

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

zbMATH Keywords

complex hyperbolic spacereal hyperbolic spacelocal Pompein transform

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15)

Related Items

Inversion Theorems for the local Pompeiu transformation in the quaternion hyperbolic space ⋮ A local two-radii theorem for quasianalytic classes of functions ⋮ On functions with given spherical means on symmetric spaces ⋮ ON ONE ZALCMAN PROBLEM FOR THE MEAN VALUE OPERATOR ⋮ Inversion of a Convolution Operator Associated with Spherical Means ⋮ Unnamed Item ⋮ Convolution equations and the local Pompeiu property on symmetric spaces and on phase space associated to the Heisenberg group ⋮ Inversion of the local Pompeiu transformation on Riemannian symmetric spaces of rank one ⋮ A local two-radii theorem on the sphere ⋮ Spherical means on two-point homogeneous spaces and applications ⋮ On functions with zero spherical means of complex hyperbolic spaces

Cites Work

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• Inversion of the local Pompeiu transform
• The Paley-Wiener theorem for distributions on symmetric spaces
• A local version of the two-circles theorem
• Pompeiu's problem on symmetric spaces
• Pompeiu transforms on geodesic spheres in real analytic manifolds
• Inversion of the Pompeiu transformation in the hyperbolic disk. (Case of two disks)
• Integral representations for Jacobi polynomials and some applications
• A duality for symmetric spaces with applications to group representations
• Paley-Wiener type theorems for a differential operator connected with symmetric spaces
• Analyticity and the Pompeiu problem
• Spectral synthesis and the Pompeiu problem
• Composition Series and Intertwining Operators for the Spherical Principal Series. I
• Spherical Harmonics

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