The theory of orthogonal R-separation for Helmholtz equations

E. G. Kalnins, W. Miller

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

We develop the theory of orthogonal R-separation for the Helmholtz equation on a pseudo-Riemannian manifold and show that it, and not ordinary variable separation, is the natural analogy of additive separation for the Hamiltonian-Jacobi equation. We provide a coordinate-free characterization of R-separation in terms of commuting symmetry operators.

Original languageEnglish (US)
Pages (from-to)91-106
Number of pages16
JournalAdvances in Mathematics
Volume51
Issue number1
DOIs
StatePublished - Jan 1984

Bibliographical note

Funding Information:
One of us (W.M.) would like to thank the University of Waikato for a Postdoctoral Fellowship and kind hospitality which made this collaboration possible.

Funding Information:
in part by NSF Grant

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