## Abstract

It is shown that every orthogonal separable coordinate system for the Helmholtz equation on S_{4} leads to an R-separable system for the complex wave equation. All orthogonal separable systems on S_{4} are classified and each is characterized by a commuting triplet of operators from the enveloping algebra of o(5). A consequence of the classification is that the most general cyclidic coordinates for the wave equation arise from ellipsoidal coordinates on S_{4}.

Original language | English (US) |
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Pages (from-to) | 449-469 |

Number of pages | 21 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 83 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1981 |

### Bibliographical note

Funding Information:supported by NSF Grant MCS 76-04838 AOI.

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