Abstract
It is shown that every orthogonal separable coordinate system for the Helmholtz equation on S4 leads to an R-separable system for the complex wave equation. All orthogonal separable systems on S4 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 S4.
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.