The theory of orthogonal R-separation for Helmholtz equations

E. G. Kalnins; W. Miller

doi:10.1016/0001-8708(84)90004-5

The theory of orthogonal R-separation for Helmholtz equations

E. G. Kalnins
, W. Miller

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

21 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 language	English (US)
Pages (from-to)	91-106
Number of pages	16
Journal	Advances in Mathematics
Volume	51
Issue number	1
DOIs	https://doi.org/10.1016/0001-8708(84)90004-5
State	Published - Jan 1984
Externally published	Yes

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

Publisher link

10.1016/0001-8708(84)90004-5

Find It

Find It at U of M Libraries

Cite this

@article{b358b74602214bb3bfe77bc1e3e78ee5,

title = "The theory of orthogonal R-separation for Helmholtz equations",

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.",

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

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",

year = "1984",

month = jan,

doi = "10.1016/0001-8708(84)90004-5",

language = "English (US)",

volume = "51",

pages = "91--106",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - The theory of orthogonal R-separation for Helmholtz equations

AU - Kalnins, E. G.

AU - Miller, W.

N1 - 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

PY - 1984/1

Y1 - 1984/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0346566153

UR - https://www.scopus.com/pages/publications/0346566153#tab=citedBy

U2 - 10.1016/0001-8708(84)90004-5

DO - 10.1016/0001-8708(84)90004-5

M3 - Article

AN - SCOPUS:0346566153

SN - 0001-8708

VL - 51

SP - 91

EP - 106

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

The theory of orthogonal R-separation for Helmholtz equations

Abstract

Bibliographical note

Publisher link

Find It

Other files and links

Fingerprint

Cite this