Pompeiu problem on product of Heisenberg groups

DOI10.1007/s11785-010-0049-6zbMath1227.32003OpenAlexW2017375469MaRDI QIDQ601084

Wayne M. Eby, Der-Chen E. Chang

Publication date: 3 November 2010

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-010-0049-6

zbMATH Keywords

Laguerre functionsspherical functionsHeisenberg groupPompeiu problemMorera propertyquadratic CR manifolds

Mathematics Subject Classification ID

Holomorphic functions of several complex variables (32A10) Harmonic analysis of several complex variables (32A50)

Cites Work

• Pompeiu problem for the Heisenberg ball
• Pompeiu problem for sets of higher codimension in Euclidean and Heisenberg settings
• Injectivity of the Pompeiu transform in the Heisenberg group
• Spherical means and CR functions on the Heisenberg group
• Estimates for spectral projection operators of the sub-Laplacian on the Heisenberg group
• Moment versions of the Morera problem in \(\mathbb C^n\) and \(\mathbb H^n\).
• Hamilton-Jacobi theory and the heat kernel on Heisenberg groups
• \(L^p\) results for the Pompeiu problem with moments on the Heisenberg group
• A Morera type theorem for \(L^ 2\) functions in the Heisenberg group
• Analyticity and the Pompeiu problem
• Mean values and differential equations
• Tauberian theorem for m‐spherical transforms on the Heisenberg group
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