The injectivity of the Pompeiu transform and \(L^ p\)-analogues of the Wiener-Tauberian theorem

DOI10.1007/BF02761653zbMath0876.43002OpenAlexW1979725778WikidataQ122646728 ScholiaQ122646728MaRDI QIDQ1903118

Rama Rawat, Alladi Sitaram

Publication date: 20 November 1997

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

Full work available at URL: https://doi.org/10.1007/bf02761653

zbMATH Keywords

affine spacetransformation groupWiener-Tauberian theoremPompeiu transformJFM 55.0138.04

Mathematics Subject Classification ID

(L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items (15)

A theorem of the Wiener-Tauberian type for \(L^ 1(H^ n)\) ⋮ The two-sided Pompeiu problem for discrete groups ⋮ Interpolation problems for functions with zero ball means ⋮ The Pompeiu problem and discrete groups ⋮ Approximation by spherical waves in \(L^p\)-spaces ⋮ On the admissible asymptotic behavior of the functions with zero integrals over the geodesic lines on a sphere ⋮ On the injectivity of integral operators related to the Euler-Poisson-Darboux equation and shifted \(k\)-plane transforms ⋮ Analogs of the Liouville property for harmonic functions on unbounded domains ⋮ The pompeiu problem ⋮ \(L^p\)-integrability, dimensions of supports of Fourier transforms and applications ⋮ Interpolation problems for functions with zero integrals over balls of fixed radius ⋮ \(L^{p}\) Wiener-Tauberian theorems for \(M(2)\) ⋮ Continuous extension of functions from a segment to functions in \(\mathbb{R}^n\) with zero ball means ⋮ Wiener-type Tauberian theorems for Fourier hyperfunctions ⋮ Characterization of eigenfunctions of the Laplace-Beltrami operator through heat propagation in small time

Cites Work

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• The Pompeiu problem revisited
• Some remarks on measures on non-compact semi-simple Lie groups
• Fourier analysis and determining sets for Radon measures on \({\mathbb{R}}^ n\)
• On an analogue of the Wiener-Tauberian theorem for symmetric spaces of the noncompact type
• Pompeiu's problem on symmetric spaces
• Injectivity of the Pompeiu transform in the Heisenberg group
• Spherical means and CR functions on the Heisenberg group
• A note on a problem of D. Pompeiu
• Spectral synthesis and the Pompeiu problem
• Offbeat Integral Geometry

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