## Abstract

The paper is devoted to the following problem. Consider the set of all radial functions with centers at the points of a closed surface in R^{n}. Are such functions complete in the space L^{q}(R^{n})? It is shown that the answer is positive if and only if q is not less than 2n/(n + 1). A similar question is also answered for Riemannian symmetric spaces of rank 1. Relations of this problem with the wave and heat equations are also discussed.

Original language | English |
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Pages (from-to) | 365-383 |

Number of pages | 19 |

Journal | Journal of Geometric Analysis |

Volume | 6 |

Issue number | 3 |

DOIs | |

State | Published - 1996 |

## Keywords

- Heat equation
- Radon transform
- Spherical waves
- Wave equation

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