The wave equation and separation of variables on the complex sphere S4

E. G. Kalnins; Willard Miller

doi:10.1016/0022-247X(81)90135-9

The wave equation and separation of variables on the complex sphere S₄

E. G. Kalnins
, Willard Miller

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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)
Pages (from-to)	449-469
Number of pages	21
Journal	Journal of Mathematical Analysis and Applications
Volume	83
Issue number	2
DOIs	https://doi.org/10.1016/0022-247X(81)90135-9
State	Published - Oct 1981
Externally published	Yes

Bibliographical note

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

Publisher link

10.1016/0022-247X(81)90135-9

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Cite this

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title = "The wave equation and separation of variables on the complex sphere S4",

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.",

author = "Kalnins, \{E. G.\} and Willard Miller",

note = "Funding Information: supported by NSF Grant MCS 76-04838 AOI.",

year = "1981",

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Y1 - 1981/10

N2 - 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.

AB - 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.

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