2007 / September Volume 2 No.3
Pompeiu problem for complex ellipsoids on the Heisenberg group
Published Date |
2007 / September
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Title | Pompeiu problem for complex ellipsoids on the Heisenberg group |
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Pagination | 731-768 |
Abstract | We extend results of the Pompeiu problem on the Heisenberg group $\mathbf{H}^n$ from spheres to complex ellipsoids. These results
also tell us what happens for spheres and complex ellipsoids on the anisotropic Heisenberg group, $\mathbf{H}^n_\mathbf{a}$
. The results for $L^2$, $L^p$, and $L^\infty$ have the same character as previous results for spheres on $\mathbf{H}^n$. However, when moving to $L^\infty$ and including rotations, we
maintain the result from Euclidean space that only one complex ellipsoid is needed.
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AMS Subject Classification |
32A10, 30E99
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Received |
2006-11-21
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