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7. N.M. Atakishiyev, G.S. Pogosyan, K.B. Wolf, A. Yakhno, Spherical geometry, Zernike’s
separability, and interbasis expansion coefficients. J. Math. Phys. 60, 101701 (2019)
8. R.L. Anderson, K.B. Wolf, Complete sets of functions on homogeneous spaces with compact
stabilizers. J. Math. Phys. 11, 3176–3183 (1970)
9. C. Grosche, Kh.H. Karayan, G.S. Pogosyan, A.N. Sissakian, Quantum motion on the threedimensional sphere: the ellipso-cylindrical basis. J. Phys. A Math. Gen. 30, 1629–1657 (1997)
10. A.A. Izmest’ev, G.S. Pogosyan, A.N. Sissakian, P. Winternitz, Contraction of Lie algebras and
separation of variables. N -dimensional sphere. J. Math. Phys. 40, 1549–1573 (1999)
11. E.G. Kalnins, W. Miller Jr., Separation of variables on n-dimensional Riemannian manifolds.
I. The n-sphere S n and Euclidean n-space R n . J. Math. Phys. 27, 1721–1736 (1986). https://
doi.org/10.1063/1.527088
12. G.S. Pogosyan, A.N. Sissakian, P. Winternitz, Separation of variables and Lie algebra
contractions. Applications to special functions. Phys. Part. Nuclei 33(Suppl. 1), S123–S144
(2002)
13. W. Miller Jr., E.G. Kalnins, G.S. Pogosyan, Exact and quasi-exact solvability of second-order
superintegrable systems. I. Euclidean space preliminaries. J. Math. Phys. 47, 033502 (2006)
14. N.M. Atakishiyev, G.S. Pogosyan, K.B. Wolf, A. Yakhno, Elliptic basis for the Zernike system:
Heun function solutions. J. Math. Phys. 59, 073503 (2018). https://doi.org/10.1063/1.5030759
15. N.M. Atakishiyev, G.S. Pogosyan, K.B. Wolf, A. Yakhno, On elliptic trigonometric form of
the Zernike system and polar limits. Phys. Scr. 94, 045202 (2019)
16. K.B. Wolf, Discrete systems and signals on phase space. Appl. Math. Inf. Sci. 4, 141–181
(2010)
17. E. Celeghini, M. Gadella, M.A. del Olmo, Zernike functions, rigged Hilbert spaces, and
potential applications. J. Math. Phys. 60, 083508 (2019). https://doi.org/10.1063/1.5093488
18. P.W. Higgs, Dynamical symmetries in a spherical geometry. J. Phys. A: Math. Gen. 12,
309–323 (1979)
19. E.G. Kalnins, J.M. Kress, W. Miller Jr., Separation of Variables and Superintegrability. The
Symmetry of Solvable Systems. (IOP Publishing, Bristol, 2018)
177
6. N.M. Atakishiyev, G.S. Pogosyan, K.B. Wolf, A. Yakhno, Interbasis expansions in the Zernike
system. J. Math. Phys. 58, 103505 (2017)
7. N.M. Atakishiyev, G.S. Pogosyan, K.B. Wolf, A. Yakhno, Spherical geometry, Zernike’s
separability, and interbasis expansion coefficients. J. Math. Phys. 60, 101701 (2019)
8. R.L. Anderson, K.B. Wolf, Complete sets of functions on homogeneous spaces with compact
stabilizers. J. Math. Phys. 11, 3176–3183 (1970)
9. C. Grosche, Kh.H. Karayan, G.S. Pogosyan, A.N. Sissakian, Quantum motion on the threedimensional sphere: the ellipso-cylindrical basis. J. Phys. A Math. Gen. 30, 1629–1657 (1997)
10. A.A. Izmest’ev, G.S. Pogosyan, A.N. Sissakian, P. Winternitz, Contraction of Lie algebras and
separation of variables. N -dimensional sphere. J. Math. Phys. 40, 1549–1573 (1999)
11. E.G. Kalnins, W. Miller Jr., Separation of variables on n-dimensional Riemannian manifolds.
I. The n-sphere S n and Euclidean n-space R n . J. Math. Phys. 27, 1721–1736 (1986). https://
doi.org/10.1063/1.527088
12. G.S. Pogosyan, A.N. Sissakian, P. Winternitz, Separation of variables and Lie algebra
contractions. Applications to special functions. Phys. Part. Nuclei 33(Suppl. 1), S123–S144
(2002)
13. W. Miller Jr., E.G. Kalnins, G.S. Pogosyan, Exact and quasi-exact solvability of second-order
superintegrable systems. I. Euclidean space preliminaries. J. Math. Phys. 47, 033502 (2006)
14. N.M. Atakishiyev, G.S. Pogosyan, K.B. Wolf, A. Yakhno, Elliptic basis for the Zernike system:
Heun function solutions. J. Math. Phys. 59, 073503 (2018). https://doi.org/10.1063/1.5030759
15. N.M. Atakishiyev, G.S. Pogosyan, K.B. Wolf, A. Yakhno, On elliptic trigonometric form of
the Zernike system and polar limits. Phys. Scr. 94, 045202 (2019)
16. K.B. Wolf, Discrete systems and signals on phase space. Appl. Math. Inf. Sci. 4, 141–181
(2010)
17. E. Celeghini, M. Gadella, M.A. del Olmo, Zernike functions, rigged Hilbert spaces, and
potential applications. J. Math. Phys. 60, 083508 (2019). https://doi.org/10.1063/1.5093488
18. P.W. Higgs, Dynamical symmetries in a spherical geometry. J. Phys. A: Math. Gen. 12,
309–323 (1979)
19. E.G. Kalnins, J.M. Kress, W. Miller Jr., Separation of Variables and Superintegrability. The
Symmetry of Solvable Systems. (IOP Publishing, Bristol, 2018)