An F. and M. Riesz Theorem on the Complex Sphere |
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| Authors: | Evgueni Doubtsov |
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| Affiliation: | (1) St. Petersburg Department, V.A. Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia |
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| Abstract: | Let μ be a measure on the complex sphere. Denote by μpq the projection of μ on H(p, q), the space of complex spherical harmonics. Assume that μpq = 0 if (p − 1)q ≠ 0, and ∥μ1q∥∞ → 0 as q → ∞. Then μ is absolutely continuous with respect to Lebesgue measure on the sphere. |
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