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We lay out the foundations of the theory of second-order conformal superintegrable systems.
N. Vilenkin. Special functions and the theory of group representations, (translated from the Russian, American Mathematical Society Translations, Volume 22). Amer. Math. Soc., Providence, R.I., 1968
1968
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E. G. Kalnins, and W. Miller, Jr., Lie theory and separation of variables. XI. The Euler-Poisson-Darboux equation. J. Math. Phys. 17
1976
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W. Miller, Jr. Symmetry and Separation of Variables, Addison-Wesley, Reading, Mass. 1977
1977
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J. Hietarinta, B. Grammaticos, B. Dorizzi and A. Ramani. Coupling-constant metamorphosis and duality between integrable Hamiltonian systems. Phys. Rev. Lett
1984
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C. P. Boyer, E. G. Kalnins, and W. Miller. Stäckel - equivalent integrable Hamiltonian systems. SIAM J. Math. Anal
1986
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E. G. Kalnins, and W. Miller, Jr., Killing tensors and nonorthogonal variable separation for the Hamilton-Jacobi equation. SIAM J. Math. Anal. 12
1987
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D. Stanton. An introduction to group representations and orthogonal polynomials. Orthogonal Polynomials: Theory and Practice, ed. P. Nevai, Proceedings of NATO-ASI, Columbus, 419-433, 1990
1990
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G. E. Andrews, R. Askey and R. Roy, Special Functions. Encyclopedia of Mathematics and its Applications, Cambridge University Press
1999
Earlier work this paper cites.
E. G. Kalnins, J. M. Kress, W. Miller Jr. and G. S. Pogosyan, Completeness of superintegrability in two-dimensional constant curvature spaces, J. Phys. A: Math Gen. 34
2001
Cited alongside, same era.
S. Gravel and P. Winternitz. Superintegrability with third-order integrals in quantum and classical mechanics. J. Math. Phys
2002
Cited alongside, same era.
S. Gravel. Hamiltonians separable in Cartesian coordinates and third-order inte- grals of motion. J. Math Phys
2004
Cited alongside, same era.
M. Eastwood, Higher symmetries of the Laplacian, Ann. of Math., 161
2005
Cited alongside, same era.
E. G. Kalnins, J. M. Kress and W. Miller Jr. Second order superintegrable systems in conformally flat spaces. III: 3D classical structure theory. J. Math. Phys
2005
Cited alongside, same era.
E. G. Kalnins, J. M. Kress and W. Miller Jr. Second order superintegrable systems in conformally flat spaces. V: 2D and 3D quantum systems. J. Math. Phys
2006
Later among the works it cites.
H. Volkmer, Generalized Ellipsoidal and Sphero-Conal Harmonics. SIGMA
2006
Later among the works it cites.
E. G. Kalnins, J. M. Kress and W. Miller Jr. Nondegenerate 3D complex Euclidean superintegrable systems and algebraic varieties, J. Math. Phys
2007
Later among the works it cites.
E. G. Kalnins, W. Miller Jr and S. Post, Wilson polynomials and the generic superintegrable system on the 2-sphere, J. Phys. A: Math. Theor
2007
Later among the works it cites.
E. G. Kalnins, W. Miller Jr. and S. Post, Models for the 3D singular isotropic oscillator quadratic algebra, Physics of Atomic Nuclei
2009
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C. Chanu and G. Rastelli. Fixed Energy R-separation for Schroedinger equation. International Journal on Geometric Methods in Modern Physics
2006
Cited alongside, same era.
E. G. Kalnins, J. M. Kress and W. Miller Jr. Second order superintegrable systems in conformally flat spaces. IV: The classical 3D Stäckel transform and 3D classification theory. J. Math. Phys
2006
Cited alongside, same era.
M. Bôcher. Über die Riehenentwickelungen der Potentialtheorie. Teubner
Cited in the paper.
I. Marquette. Superintegrabilite avec integrales d’order trois, algebras polynomiales et mechanique quantique supersymetrique. PhD thesis, University of Montreal, 2009
2009
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S. Post, University of Minnesota Ph.D. Thesis, Second order superintegrable systems. 2009
2009
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