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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF
Book Information:

Author: Willard Miller Jr.
Title: Symmetry and separation of variables
Additional book information: Addison-Wesley Publishing Company, Reading, Massachusetts, 1977, xxx + 285 pp., $21.50.

References [Enhancements On Off] (What's this?)

  • 1. M. Bôcher, Die Reihenentwickelungen der Potentialtheorie, Leipzig, 1894.
  • 2. Luther Pfahler Eisenhart, Separable systems of Stackel, Ann. of Math. (2) 35 (1934), no. 2, 284–305. MR 1503163, 10.2307/1968433
  • 3. Peter Havas, Separation of variables in the Hamilton-Jacobi, Schrödinger, and related equations. I. Complete separation, J. Mathematical Phys. 16 (1975), 1461–1468. MR 0403463
  • 4. E. G. Kalnins and W. Miller Jr., Lie theory and the wave equation in space-time. V. 𝑅-separable solutions of the wave equation 𝜓_{𝑡𝑡}-Δ₃𝜓=0, J. Mathematical Phys. 19 (1978), no. 6, 1247–1257. MR 0507313
  • 5. W. Miller, J. Patera and P. Winternitz, Subgroups of Lie groups and separation of variables. Report CRM-813, Centre de Recherches Mathématiques, Université de Montréal, 1978.
  • 6. Parry Moon and Domina Eberle Spencer, Field theory handbook. Including coordinate systems, differential equations and their solution, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0136092
  • 7. Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774
  • 8. Heinz-Dieter Niessen, Algebraische Untersuchungen über separierbare Operatoren, Math. Z. 94 (1966), 328–348 (German). MR 0211055
  • 9. M. N. Olevskiĭ, Triorthogonal systems in spaces of constant curvature in which the equation Δ₂𝑢+𝜆𝑢=0 allows a complete separation of variables, Mat. Sbornik N.S. 27(69) (1950), 379–426 (Russian). MR 0038535
  • 10. H. P. Robertson, Bemerkung über separierbare Systeme in der Wellenmechanik, Math. Ann. 98 (1928), no. 1, 749–752 (German). MR 1512435, 10.1007/BF01451624
  • 11. P. Stäckel, Über die Integration der Hamilton-Jacobischen Differentialgleichung mittels Separation der Variabelen, Habilitationsschrift, Halle, 1891.
  • 12. P. Winternitz and I. Friš, Invariant expansions of relativistic amplitudes and subgroups of the proper Lorentz group, Soviet J. Nuclear Phys. 1 (1965), 636–643. MR 0202919
  • 13. E. G. Kalnins and Willard Miller Jr., Killing tensors and variable separation for Hamilton-Jacobi and Helmholtz equations, SIAM J. Math. Anal. 11 (1980), no. 6, 1011–1026. MR 595827, 10.1137/0511089

Review Information:

Reviewer: Tom H. Koornwinder
Journal: Bull. Amer. Math. Soc. 1 (1979), 1014-1019
DOI: https://doi.org/10.1090/S0273-0979-1979-14723-2