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Miller, Willard jun.

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Author ID: miller.willard-jun Recent zbMATH articles by "Miller, Willard jun."
Published as: Miller Jr., Willard; Miller, W.; Miller, W. jun; Miller, W. jun.; Miller, Willard; Miller, Willard jun.
Homepage: https://www.ima.umn.edu/~miller/
External Links: ORCID
Documents Indexed: 202 Publications since 1964, including 11 Books

Publications by Year

Citations contained in zbMATH Open

168 Publications have been cited 1,692 times in 905 Documents Cited by Year
Lie theory and special functions. Zbl 0174.10502
Miller, W. jun.
136
1968
Symmetry groups and their applications. Zbl 0306.22001
Miller, Willard jun.
95
1972
Classical and quantum superintegrability with applications. Zbl 1276.81070
Miller, Willard jun.; Post, Sarah; Winternitz, Pavel
75
2013
Completeness of superintegrability in two-dimensional constant-curvature spaces. Zbl 0993.70014
Kalnins, E. G.; Kress, J. M.; Pogosyan, G. S.; Miller, W. jun.
51
2001
Killing tensors and variable separation for Hamilton-Jacobi and Helmholtz equations. Zbl 0454.70023
Kalnins, E. G.; Miller, Willard jun.
40
1980
Superintegrable systems in Darboux spaces. Zbl 1063.37050
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.; Winternitz, P.
34
2003
Second-order superintegrable systems in conformally flat spaces. I: Two-dimensional classical structure theory. Zbl 1110.37054
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
31
2005
Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions. Zbl 0862.35099
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
31
1996
Second order superintegrable systems in conformally flat spaces. IV: The classical 3D Stäckel transform and 3D classification theory. Zbl 1112.37058
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
27
2006
Separation of variables on \(n\)-dimensional Riemannian manifolds. I: The \(n\)-sphere \(S^n\), and Euclidean \(n\)-space \(R^n\). Zbl 0602.35014
Kalnins, E. G.; Miller, W. jun.
27
1986
The group O(4), separation of variables and the hydrogen atom. Zbl 0335.35002
Kalnins, E. G.; Miller, W. jun.; Winternitz, P.
27
1976
Symmetry and separation of variables for the Helmholtz and Laplace equations. Zbl 0314.33011
Boyer, C. P.; Kalnins, E. G.; Miller, W. jun.
25
1976
Killing tensors and nonorthogonal variable separation for Hamilton-Jacobi equations. Zbl 0466.70024
Kalnins, E. G.; Miller, Willard jun.
24
1981
Symmetry and separation of variables. With a foreword by Richard Askey. Zbl 0368.35002
Miller, Willard jun.
24
1977
Second order superintegrable systems in conformally flat spaces. III: Three-dimensional classical structure theory. Zbl 1111.37055
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
23
2005
Families of orthogonal and biorthogonal polynomials on the n-sphere. Zbl 0727.33002
Kalnins, E. G.; Miller, Willard jun.; Tratnik, M. V.
23
1991
Wilson polynomials and the generic superintegrable system on the 2-sphere. Zbl 1121.37052
Kalnins, E. G.; Miller, W. jun.; Post, S.
22
2007
Second-order superintegrable systems in conformally flat spaces. V: Two- and three-dimensional quantum systems. Zbl 1112.81051
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
22
2006
Complete sets of commuting operators and 0(3) scalars in the enveloping algebra of SU(3). Zbl 0289.22019
Judd, B. R.; Miller, W. jun.; Patera, J.; Winternitz, P.
22
1974
Second order superintegrable systems in conformally flat spaces. II: The classical two-dimensional Stäckel transform. Zbl 1110.37055
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
21
2005
Matrix operator symmetries of the Dirac equation and separation of variables. Zbl 0615.35075
Kalnins, E. G.; Miller, W. jun.; Williams, G. C.
21
1986
Lie theory and separation of variables. V. The equations \(iU_t+U_{xx}=0\) and \(iU_t+U_{xx}-c/x^2U=0\). Zbl 0286.35025
Kalnins, E. G.; Miller, W. jun.
21
1974
Symmetries of differential equations. The hypergeometric and Euler- Darboux equations. Zbl 0254.35080
Miller, Willard jun.
20
1973
Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials. Zbl 1293.33013
Kalnins, Ernest G.; Miller, Willard jun.; Post, Sarah
19
2013
Lie theory and separation of variables. VI: The equation \(iU_t+ \Delta_2 U=0\). Zbl 0295.35020
Boyer, C. P.; Kalnins, E. G.; Miller, W. jun.
19
1975
Superintegrability in three-dimensional Euclidean space. Zbl 1059.81525
Kalnins, E. G.; Williams, G. C.; Miller, W. jun.; Pogosyan, G. S.
18
1999
Canonical equations and symmetry techniques for q-series. Zbl 0624.33005
Agarwal, A. K.; Kalnins, E. G.; Miller, Willard jun.
18
1987
Symmetry techniques for q-series: Askey-Wilson polynomials. Zbl 0695.33008
Kalnins, E. G.; Miller, Willard jun.
17
1989
Lie theory and generalizations of the hypergeometric functions. Zbl 0269.33007
Miller, Willard jun.
17
1973
Stäckel-equivalent integrable Hamiltonian systems. Zbl 0607.58015
Boyer, C. P.; Kalnins, E. G.; Miller, W. jun.
16
1986
Completeness of multiseparable superintegrability on the complex 2-sphere. Zbl 0963.81070
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
15
2000
Completeness of multiseparable superintegrability in \(E_{2,C}\). Zbl 0954.81009
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
15
2000
Models of \(q\)-algebra representations: Tensor products of special unitary and oscillator algebras. Zbl 0780.17014
Kalnins, E. G.; Manocha, H. L.; Miller, Willard jun.
15
1992
Superintegrability of the two-dimensional hyperboloid. Zbl 0895.58049
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
14
1997
Models of \(Q\)-algebra representations: The group of plane motions. Zbl 0805.33020
Kalnins, E. G.; Miller, W. jun.; Mukherjee, S.
14
1994
Models of \(q\)-algebra representations: Matrix elements of the \(q\)- oscillator algebra. Zbl 0795.17022
Kalnins, E. G.; Miller, Willard jun.; Mukherjee, Sanchita
14
1993
Separation of variables for complex Riemannian spaces of constant curvature. I: Orthogonal separable coordinates for \(S_{n{\mathbb{C}}}\) and \(E_{n{\mathbb{C}}}\). Zbl 0543.53014
Kalnins, E. G.; Miller, W. jun.; Reid, G. J.
14
1984
Lie theory and \(q\)-difference equations. Zbl 0206.39001
Miller, W. jun.
14
1970
Lie theory and difference equations. I. Zbl 0193.06404
Miller, W. jun.
14
1969
Some applications of the representation theory of the Euclidean group in three-space. Zbl 0136.29901
Miller, W. jun.
13
1964
Coulomb-oscillator duality in spaces of constant curvature. Zbl 0987.81024
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
12
2000
Subgroups of Lie groups and separation of variables. Zbl 0476.58021
Miller, W. jun.; Patera, J.; Winternitz, P.
12
1981
Lie theory and separation of variables. IX: Orthogonal \(R\)-separable coordinate systems for the wave equation \(\Psi_{tt}-\Delta_2\Psi=0\). Zbl 0324.35053
Kalnins, E. G.; Miller, W. jun.
12
1976
Exact and quasiexact solvability of second-order superintegrable quantum systems. I: Euclidean space preliminaries. Zbl 1111.81086
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
11
2006
Functional separation of variables for Laplace equations in two dimensions. Zbl 0807.58045
Miller, W. jun.; Rubel, Lee A.
11
1993
q-series and orthogonal polynomials associated with Barnes’ first lemma. Zbl 0652.33007
Kalnins, E. G.; Miller, Willard jun.
11
1988
A recurrence relation approach to higher order quantum superintegrability. Zbl 1217.81105
Kalnins, Ernie G.; Kress, Jonathan M.; Miller, Willard jun.
10
2011
Families of classical subgroup separable superintegrable systems. Zbl 1184.37053
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
10
2010
Coupling constant metamorphosis and \(N\)th-order symmetries in classical and quantum mechanics. Zbl 1214.37038
Kalnins, E. G.; Miller, W. jun.; Post, S.
10
2010
Conformal Killing tensors and variable separation for Hamilton-Jacobi equations. Zbl 0565.70019
Kalnins, E. G.; Miller, Willard jun.
10
1983
Lie theory and the wave equation in space-time. I: The Lorentz group. Zbl 0336.35059
Kalnins, E. G.; Miller, W. jun.
10
1977
Lie theory and separation of variables. IV: The groups SO(2,1) and SO(3). Zbl 0285.33017
Kalnins, E. G.; Miller, Willard jun.
10
1974
On superintegrable symmetry-breaking potentials in \(N\)-dimensional Euclidean space. Zbl 1066.81020
Kalnins, E. G.; Williams, G. C.; Miller, W. jun.; Pogosyan, G. S.
9
2002
Quadrics on complex Riemannian spaces of constant curvature, separation of variables, and the Gaudin magnet. Zbl 0802.58030
Kalnins, E. G.; Kuznetsov, V. B.; Miller, Willard jun.
9
1994
Hypergeometric expansions of Heun polynomials. Zbl 0744.33007
Kalnins, E. G.; Miller, W. jun.
9
1991
The Lie theory of two-variable hypergeometric functions. Zbl 0452.33019
Kalnins, E. G.; Manocha, H. L.; Miller, Willard jun.
9
1980
Lie theory and the wave equation in space-time. III: Semisubgroup coordinates. Zbl 0345.35064
Kalnins, E. G.; Miller, W. jun.
9
1977
Lie theory and separation of variables. III: The equation \(f_{tt}-f_{ss}= \gamma^2 f\). Zbl 0285.33016
Kalnins, E. G.; Miller, W. jun.
9
1974
Lie theory and separation of variables. I: Parabolic cylinder coordinates. Zbl 0283.33012
Miller, Willard jun.
9
1974
Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere. Zbl 1217.81106
Kalnins, Ernie G.; Miller, Willard jun.; Post, Sarah
8
2011
Superintegrability and higher order integrals for quantum systems. Zbl 1192.81129
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
8
2010
Superintegrability in classical and quantum systems. Proceedings of a workshop, Montréal, Canada, September 16–21, 2002. Zbl 1055.37004
Tempesta, P. (ed.); Winternitz, P. (ed.); Harnad, J. (ed.); Miller, W. jun. (ed.); Pogosyan, G. (ed.); Rodriguez, M. (ed.)
8
2004
Superintegrability on the two-dimensional hyperboloid. II. Zbl 0962.81007
Kalnins, E. G.; Miller, W. jun.; Hakobyan, Ye. M.; Pogosyan, G. S.
8
1999
Differential-Stäckel matrices. Zbl 0586.35008
Kalnins, E. G.; Miller, Willard jun.
8
1985
Lie theory and separation of variables. XI: The EPD equation. Zbl 0324.35055
Kalnins, E. G.; Miller, Willard jun.
8
1976
Lie theory and the Appell functions \(F_1\). Zbl 0235.33017
Miller, Willard jun.
8
1973
On the special function theory of occupation number space. Zbl 0138.38304
Miller, Willard jun.
8
1965
Toward a classification of semidegenerate 3D superintegrable systems. Zbl 1361.81065
Escobar-Ruiz, M. A.; Miller, Willard jun.
7
2017
Bôcher contractions of conformally superintegrable Laplace equations. Zbl 1338.81228
Kalnins, Ernest G.; Miller, Willard jun.; Subag, Eyal
7
2016
Integrability, Stäckel spaces, and rational potentials. Zbl 0880.70013
Kalnins, E. G.; Benenti, S.; Miller, Willard jun.
7
1997
Models of \(q\)-algebra representations: Matrix elements of \(U_ q(su_ 2)\). Zbl 0815.33012
Kalnins, E. G.; Miller, Willard jun.; Mukherjee, Sanchita
7
1994
Lie theory and the wave equation in space-time. IV: The Klein-Gordon equation and the Poincaré group. Zbl 0383.35037
Kalnins, E. G.; Miller, W. jun.
7
1978
Quadratic algebra contractions and second-order superintegrable systems. Zbl 1300.22013
Kalnins, Ernest G.; Miller, W. jun.
6
2014
Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties. Zbl 1128.37037
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
6
2007
Complete sets of invariants for dynamical systems that admit a separation of variables. Zbl 1060.70027
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.; Pogosyan, G. S.
6
2002
Models of \(q\)-algebra representations: \(q\)-integral transforms and “addition theorems”. Zbl 0817.17019
Kalnins, E. G.; Miller, Willard jun.
6
1994
A note on Wilson polynomials. Zbl 0619.33008
Miller, Willard jun.
6
1987
Lie theory and separation of variables. VIII: Semisubgroup coordinates for \(\Psi_{tt}-\Delta_2\Psi =0\). Zbl 0321.35049
Kalnins, E. G.; Miller, Willard jun.
6
1975
On Lie algebras and some special functions of mathematical physics. Zbl 0132.29602
Miller, W. jun.
6
1964
Structure relations and Darboux contractions for 2D 2nd order superintegrable systems. Zbl 1317.22013
Heinonen, Robin; Kalnins, Ernest G.; Miller, Willard jun.; Subag, Eyal
5
2015
The mathematics of signal processing. Zbl 1257.94001
Damelin, Steven B.; Miller, Willard jun.
5
2012
Fine structure for 3D second-order superintegrable systems: three-parameter potentials. Zbl 1114.37032
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
5
2007
Killing-Yano tensors and variable separation in Kerr geometry. Zbl 0696.53044
Kalnins, E. G.; Miller, W. jun.; Williams, G. C.
5
1989
The general theory of R-separation for Helmholtz equations. Zbl 0514.58038
Kalnins, E. G.; Miller, W. jun.
5
1983
Harmonic analysis and expansion formulas for two-variable hypergeometric functions. Zbl 0493.33004
Kalnins, E. G.; Manocha, H. L.; Miller, Willard jun.
5
1982
Non-orthogonal separable coordinate systems for the flat 4-space Helmholtz equation. Zbl 0422.35022
Kalnins, E. G.; Miller, Willard jun.
5
1979
R-separable coordinates for three-dimensional complex Riemannian spaces. Zbl 0391.22012
Boyer, C. P.; Kalnins, E. G.; Miller, Willard jun.
5
1978
Symmetry and separation of variables for the Hamilton-Jacobi equation \(W^2_t-W^2_x-W^2_y=0\). Zbl 0365.70021
Boyer, C. P.; Kalnins, E. G.; Miller, W. jun
5
1978
Lie theory and the wave equation in space-time. II: The group \(SO(4,\mathbb{C})\). Zbl 0345.35063
Kalnins, E. G.; Miller, Willard jun.
5
1978
The wave equation, O(2,2), and separation of variables on hyperboloids. Zbl 0412.35055
Kalnins, E. G.; Miller, W. jun.
5
1977
Lie theory and separation of variables. II: Parabolic coordinates. Zbl 0285.33015
Miller, W. jun.
5
1974
Lie theory and the Lauricella functions \(F_D\). Zbl 0243.33009
Miller, Willard jun.
5
1972
Separation of variables and superintegrability. The symmetry of solvable systems. Zbl 1416.35002
Kalnins, Ernest G.; Kress, Jonathan M.; Miller, Willard jun.
4
2018
Three-body problem in \(d\)-dimensional space: ground state, (quasi)-exact-solvability. Zbl 1384.81030
Turbiner, Alexander V.; Miller, Willard jun.; Escobar-Ruiz, M. A.
4
2018
Three-body problem in 3D space: ground state, (quasi)-exact-solvability. Zbl 1415.70024
Turbiner, Alexander V.; Miller, Willard jun.; Escobar-Ruiz, Adrian M.
4
2017
Laplace-type equations as conformal superintegrable systems. Zbl 1268.37078
Kalnins, Ernest G.; Kress, Jonathan M.; Miller, Willard jun.; Post, Sarah
4
2011
Tools for verifying classical and quantum superintegrability. Zbl 1217.81104
Kalnins, Ernest G.; Kress, Jonathan M.; Miller, Willard jun.
4
2010
Models for quadratic algebras associated with second order superintegrable systems in 2D. Zbl 1157.81012
Kalnins, Ernest G.; Miller, Willard jun.; Post, Sarah
4
2008
Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties. Zbl 1153.81383
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
4
2007
Exact and quasiexact solvability of second order superintegrable quantum systems. II: Relation to separation of variables. Zbl 1121.81067
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
4
2007
Separation of variables and superintegrability. The symmetry of solvable systems. Zbl 1416.35002
Kalnins, Ernest G.; Kress, Jonathan M.; Miller, Willard jun.
4
2018
Three-body problem in \(d\)-dimensional space: ground state, (quasi)-exact-solvability. Zbl 1384.81030
Turbiner, Alexander V.; Miller, Willard jun.; Escobar-Ruiz, M. A.
4
2018
The quantum \(n\)-body problem in dimension \(d \geqslant n - 1\): ground state. Zbl 1396.81084
Miller, Willard jun.; Turbiner, Alexander V; Escobar-Ruiz, M A
3
2018
Toward a classification of semidegenerate 3D superintegrable systems. Zbl 1361.81065
Escobar-Ruiz, M. A.; Miller, Willard jun.
7
2017
Three-body problem in 3D space: ground state, (quasi)-exact-solvability. Zbl 1415.70024
Turbiner, Alexander V.; Miller, Willard jun.; Escobar-Ruiz, Adrian M.
4
2017
Separation equations for 2D superintegrable systems on constant curvature spaces. Zbl 1375.81129
Escobar-Ruiz, M. A.; Kalnins, Ernest G.; Miller, Willard jun.
1
2017
Bôcher contractions of conformally superintegrable Laplace equations. Zbl 1338.81228
Kalnins, Ernest G.; Miller, Willard jun.; Subag, Eyal
7
2016
Conformal Laplace superintegrable systems in 2D: polynomial invariant subspaces. Zbl 1346.81050
Escobar-Ruiz, M. A.; Miller, Willard jun.
1
2016
Structure relations and Darboux contractions for 2D 2nd order superintegrable systems. Zbl 1317.22013
Heinonen, Robin; Kalnins, Ernest G.; Miller, Willard jun.; Subag, Eyal
5
2015
(Quasi)-exact-solvability on the sphere \(S^{n}\). Zbl 1318.81031
Miller, Willard; Turbiner, Alexander V.
3
2015
Examples of complete solvability of 2D classical superintegrable systems. Zbl 1331.81140
Chen, Yuxuan; Kalnins, Ernie G.; Li, Qiushi; Miller, Willard jun.
2
2015
Quadratic algebra contractions and second-order superintegrable systems. Zbl 1300.22013
Kalnins, Ernest G.; Miller, W. jun.
6
2014
Particle in a field of two centers in prolate spheroidal coordinates: integrability and solvability. Zbl 1291.81139
Miller, Willard jun.; Turbiner, Alexander V.
2
2014
Classical and quantum superintegrability with applications. Zbl 1276.81070
Miller, Willard jun.; Post, Sarah; Winternitz, Pavel
75
2013
Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials. Zbl 1293.33013
Kalnins, Ernest G.; Miller, Willard jun.; Post, Sarah
19
2013
Extended Kepler–Coulomb quantum superintegrable systems in three dimensions. Zbl 1264.81183
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
3
2013
The mathematics of signal processing. Zbl 1257.94001
Damelin, Steven B.; Miller, Willard jun.
5
2012
Solutions of Helmholtz and Schrödinger equations with side condition and nonregular separation of variables. Zbl 1291.35244
Broadbridge, Philip; Chanu, Claudia M.; Miller, Willard jun.
1
2012
Superintegrability in a non-conformally-flat space. Zbl 1267.81141
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
1
2012
Structure theory for extended Kepler-Coulomb 3D classical superintegrable systems. Zbl 1242.81094
Kalnins, Ernie G.; Miller, Willard jun.
1
2012
A recurrence relation approach to higher order quantum superintegrability. Zbl 1217.81105
Kalnins, Ernie G.; Kress, Jonathan M.; Miller, Willard jun.
10
2011
Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere. Zbl 1217.81106
Kalnins, Ernie G.; Miller, Willard jun.; Post, Sarah
8
2011
Laplace-type equations as conformal superintegrable systems. Zbl 1268.37078
Kalnins, Ernest G.; Kress, Jonathan M.; Miller, Willard jun.; Post, Sarah
4
2011
Symmetry and separation of variables. With a foreword by Richard Askey. Reprint of the 1977 hardback ed. Zbl 1223.35006
Miller, Willard jun.
2
2011
Families of classical subgroup separable superintegrable systems. Zbl 1184.37053
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
10
2010
Coupling constant metamorphosis and \(N\)th-order symmetries in classical and quantum mechanics. Zbl 1214.37038
Kalnins, E. G.; Miller, W. jun.; Post, S.
10
2010
Superintegrability and higher order integrals for quantum systems. Zbl 1192.81129
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
8
2010
Tools for verifying classical and quantum superintegrability. Zbl 1217.81104
Kalnins, Ernest G.; Kress, Jonathan M.; Miller, Willard jun.
4
2010
Structure theory for second order 2D superintegrable systems with 1-parameter potentials. Zbl 1195.81070
Kalnins, Ernest G.; Kress, Jonathan M.; Miller, Willard jun.; Post, Sarah
2
2009
Models for quadratic algebras associated with second order superintegrable systems in 2D. Zbl 1157.81012
Kalnins, Ernest G.; Miller, Willard jun.; Post, Sarah
4
2008
Wilson polynomials and the generic superintegrable system on the 2-sphere. Zbl 1121.37052
Kalnins, E. G.; Miller, W. jun.; Post, S.
22
2007
Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties. Zbl 1128.37037
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
6
2007
Fine structure for 3D second-order superintegrable systems: three-parameter potentials. Zbl 1114.37032
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
5
2007
Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties. Zbl 1153.81383
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
4
2007
Exact and quasiexact solvability of second order superintegrable quantum systems. II: Relation to separation of variables. Zbl 1121.81067
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
4
2007
Second order superintegrable systems in conformally flat spaces. IV: The classical 3D Stäckel transform and 3D classification theory. Zbl 1112.37058
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
27
2006
Second-order superintegrable systems in conformally flat spaces. V: Two- and three-dimensional quantum systems. Zbl 1112.81051
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
22
2006
Exact and quasiexact solvability of second-order superintegrable quantum systems. I: Euclidean space preliminaries. Zbl 1111.81086
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
11
2006
Second-order superintegrable systems in conformally flat spaces. I: Two-dimensional classical structure theory. Zbl 1110.37054
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
31
2005
Second order superintegrable systems in conformally flat spaces. III: Three-dimensional classical structure theory. Zbl 1111.37055
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
23
2005
Second order superintegrable systems in conformally flat spaces. II: The classical two-dimensional Stäckel transform. Zbl 1110.37055
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.
21
2005
Jacobi, ellipsoidal coordinates and superintegrable systems. Zbl 1080.35150
Kalnins, E. G.; Kress, J. M.; Miller, W.
3
2005
Jacobi elliptic coordinates, functions of Heun and Lamé type and the Niven transform. Zbl 1133.33302
Kalnins, E. G.; Miller, W. jun.
1
2005
Second order superintegrable systems in three dimensions. Zbl 1128.37038
Miller, Willard
1
2005
Superintegrability in classical and quantum systems. Proceedings of a workshop, Montréal, Canada, September 16–21, 2002. Zbl 1055.37004
Tempesta, P. (ed.); Winternitz, P. (ed.); Harnad, J. (ed.); Miller, W. jun. (ed.); Pogosyan, G. (ed.); Rodriguez, M. (ed.)
8
2004
Superintegrable systems in Darboux spaces. Zbl 1063.37050
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.; Winternitz, P.
34
2003
On superintegrable symmetry-breaking potentials in \(N\)-dimensional Euclidean space. Zbl 1066.81020
Kalnins, E. G.; Williams, G. C.; Miller, W. jun.; Pogosyan, G. S.
9
2002
Complete sets of invariants for dynamical systems that admit a separation of variables. Zbl 1060.70027
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.; Pogosyan, G. S.
6
2002
Completeness of superintegrability in two-dimensional constant-curvature spaces. Zbl 0993.70014
Kalnins, E. G.; Kress, J. M.; Pogosyan, G. S.; Miller, W. jun.
51
2001
Completeness of multiseparable superintegrability on the complex 2-sphere. Zbl 0963.81070
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
15
2000
Completeness of multiseparable superintegrability in \(E_{2,C}\). Zbl 0954.81009
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
15
2000
Coulomb-oscillator duality in spaces of constant curvature. Zbl 0987.81024
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
12
2000
Special functions and perturbations of black holes. Zbl 1097.83520
Kalnins, E. G.; Miller, W. jun.; Torres del Castillo, G. F.; Williams, G. C.
1
2000
Multiseparability and superintegrability for classical and quantum systems. Zbl 0967.37032
Miller, W. jun.
1
2000
Superintegrability in three-dimensional Euclidean space. Zbl 1059.81525
Kalnins, E. G.; Williams, G. C.; Miller, W. jun.; Pogosyan, G. S.
18
1999
Superintegrability on the two-dimensional hyperboloid. II. Zbl 0962.81007
Kalnins, E. G.; Miller, W. jun.; Hakobyan, Ye. M.; Pogosyan, G. S.
8
1999
Contractions of Lie algebras: Applications to special functions and separation of variables. Zbl 0940.33007
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
4
1999
Superintegrability of the two-dimensional hyperboloid. Zbl 0895.58049
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
14
1997
Integrability, Stäckel spaces, and rational potentials. Zbl 0880.70013
Kalnins, E. G.; Benenti, S.; Miller, Willard jun.
7
1997
Tensor products of \(q\)-superalgebra representations and \(q\)-series identities. Zbl 0929.33016
Chung, Won Sang; Kalnins, E. G.; Miller, W. jun.
1
1997
Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions. Zbl 0862.35099
Kalnins, E. G.; Miller, W. jun.; Pogosyan, G. S.
31
1996
A note on tensor products of \(q\)-algebra representations and orthogonal polynomials. Zbl 0864.33016
Kalnins, E. G.; Miller, Willard jun.
4
1996
Intrinsic characterization of the separation constant for spin one and gravitational perturbations in Kerr geometry. Zbl 0867.53068
Kalnins, E. G.; Williams, G. C.; Miller, W. jun.
3
1996
\(q\)-algebra representations of the Euclidean, pseudo-Euclidean and oscillator algebras, and their tensor products. Zbl 0864.33015
Kalnins, E. G.; Miller, Willard jun.
2
1996
Models of \(Q\)-algebra representations: The group of plane motions. Zbl 0805.33020
Kalnins, E. G.; Miller, W. jun.; Mukherjee, S.
14
1994
Quadrics on complex Riemannian spaces of constant curvature, separation of variables, and the Gaudin magnet. Zbl 0802.58030
Kalnins, E. G.; Kuznetsov, V. B.; Miller, Willard jun.
9
1994
Models of \(q\)-algebra representations: Matrix elements of \(U_ q(su_ 2)\). Zbl 0815.33012
Kalnins, E. G.; Miller, Willard jun.; Mukherjee, Sanchita
7
1994
Models of \(q\)-algebra representations: \(q\)-integral transforms and “addition theorems”. Zbl 0817.17019
Kalnins, E. G.; Miller, Willard jun.
6
1994
Models of \(q\)-algebra representations: Matrix elements of the \(q\)- oscillator algebra. Zbl 0795.17022
Kalnins, E. G.; Miller, Willard jun.; Mukherjee, Sanchita
14
1993
Functional separation of variables for Laplace equations in two dimensions. Zbl 0807.58045
Miller, W. jun.; Rubel, Lee A.
11
1993
Orthogonal polynomials on \(n\)-spheres: Gegenbauer, Jacobi and Heun. Zbl 0867.33005
Kalnins, E. G.; Miller, Willard jun.
1
1993
Models of \(q\)-algebra representations: Tensor products of special unitary and oscillator algebras. Zbl 0780.17014
Kalnins, E. G.; Manocha, H. L.; Miller, Willard jun.
15
1992
Recent advances in the use of separation of variables methods in general relativity. Zbl 0776.53050
Kalnins, E. G.; Miller, Willard jun.; Williams, G. C.
4
1992
Separable coordinates, integrability and the Niven equations. Zbl 0764.35081
Kalnins, E. G.; Miller, W. jun.
4
1992
A note on group contractions and radar ambiguity functions. Zbl 0764.22012
Kalnins, E. G.; Miller, W. jun.
1
1992
Families of orthogonal and biorthogonal polynomials on the n-sphere. Zbl 0727.33002
Kalnins, E. G.; Miller, Willard jun.; Tratnik, M. V.
23
1991
Hypergeometric expansions of Heun polynomials. Zbl 0744.33007
Kalnins, E. G.; Miller, W. jun.
9
1991
Complete sets of functions for perturbations of Robertson-Walker cosmologies and spin 1 equations in Robertson-Walker-type space-times. Zbl 0729.53073
Kalnins, E. G.; Miller, W. jun.
4
1991
Radar and sonar. Part I. Lecture notes from the IMA summer program ’Radar and sonar’, June 18-June 29, 1990 in Minneapolis, MN (USA). Zbl 0722.00053
Blahut, Richard E.; Miller, Willard jun.; Wilcox, Calvin H.
2
1991
Complete sets of functions for perturbations of Robertson Walker cosmologies. Zbl 0729.53074
Kalnins, E. G.; Miller, W. jun.
1
1991
Topics in harmonic analysis with applications to radar and sonar. Zbl 0753.43004
Miller, Willard jun.
1
1991
Conformal symmetries and generalized recurrences for heat and Schrödinger equations in one spatial dimension. Zbl 0763.35025
Kalnins, E. G.; Levine, Raphael D.; Miller, Willard jun.
1
1991
Separation of variables methods for systems of differential equations in mathematical physics. Zbl 0742.35048
Miller, W. jun.; Kalnins, E. G.
1
1990
Symmetry techniques for q-series: Askey-Wilson polynomials. Zbl 0695.33008
Kalnins, E. G.; Miller, Willard jun.
17
1989
Killing-Yano tensors and variable separation in Kerr geometry. Zbl 0696.53044
Kalnins, E. G.; Miller, W. jun.; Williams, G. C.
5
1989
Teukolsky-Starobinsky identities for arbitrary spin. Zbl 0709.53536
Kalnins, E. G.; Miller, W. jun.; Williams, G. C.
4
1989
q-series and orthogonal polynomials associated with Barnes’ first lemma. Zbl 0652.33007
Kalnins, E. G.; Miller, Willard jun.
11
1988
Mechanisms for variable separation in partial differential equations and their relationship to group theory. Zbl 0788.35017
Miller, Willard jun.
3
1988
Canonical equations and symmetry techniques for q-series. Zbl 0624.33005
Agarwal, A. K.; Kalnins, E. G.; Miller, Willard jun.
18
1987
A note on Wilson polynomials. Zbl 0619.33008
Miller, Willard jun.
6
1987
R-separation of variables for the time-dependent Hamilton-Jacobi and Schrödinger equations. Zbl 0645.35085
Kalnins, E. G.; Miller, Willard jun.
2
1987
Separation of variables on \(n\)-dimensional Riemannian manifolds. I: The \(n\)-sphere \(S^n\), and Euclidean \(n\)-space \(R^n\). Zbl 0602.35014
Kalnins, E. G.; Miller, W. jun.
27
1986
Matrix operator symmetries of the Dirac equation and separation of variables. Zbl 0615.35075
Kalnins, E. G.; Miller, W. jun.; Williams, G. C.
21
1986
Stäckel-equivalent integrable Hamiltonian systems. Zbl 0607.58015
Boyer, C. P.; Kalnins, E. G.; Miller, W. jun.
16
1986
Differential-Stäckel matrices. Zbl 0586.35008
Kalnins, E. G.; Miller, Willard jun.
8
1985
Generalized Stäckel matrices. Zbl 0588.35021
Kalnins, E. G.; Miller, W. jun.
4
1985
Related evolution equations and Lie symmetries. Zbl 0566.58009
Kalnins, E. G.; Miller, Willard jun.
2
1985
Separation of variables for complex Riemannian spaces of constant curvature. I: Orthogonal separable coordinates for \(S_{n{\mathbb{C}}}\) and \(E_{n{\mathbb{C}}}\). Zbl 0543.53014
Kalnins, E. G.; Miller, W. jun.; Reid, G. J.
14
1984
Conformal Killing tensors and variable separation for Hamilton-Jacobi equations. Zbl 0565.70019
Kalnins, E. G.; Miller, Willard jun.
10
1983
The general theory of R-separation for Helmholtz equations. Zbl 0514.58038
Kalnins, E. G.; Miller, W. jun.
5
1983
...and 68 more Documents
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Cited by 974 Authors

61 Miller, Willard jun.
60 Kalnins, Ernest G.
37 Winternitz, Pavel
36 Vinet, Luc
20 Marquette, Ian
18 Khan, Subuhi
16 Floreanini, Roberto
16 McLenaghan, Raymond G.
16 Pogosyan, George S.
16 Rastelli, Giovanni
15 Rañada, Manuel F.
13 Zhedanov, Alexei S.
12 Kress, Jonathan M.
11 Chanu, Claudia Maria
11 Srivastava, Hari Mohan
11 Tsyganov, Andreĭ Vladimirovich
11 Wolf, Kurt Bernardo
10 Escobar-Ruiz, Mauricio A.
10 Miller, Willar jun.
10 Santander, Mariano
9 Genest, Vincent X.
9 Patera, Jiří
9 Sahai, Vivek
8 Benenti, Sergio
8 Boyer, Charles P.
8 Cariñena, José F.
8 Quesne, Christiane
7 Atakishiev, Natig M.
7 Chossat, Pascal
7 Degiovanni, Luca
7 Fordy, Allan P.
7 Herranz, Francisco José
7 Iliev, Plamen
7 Kamran, Niky
7 Manocha, H. L.
7 Negro, Javier
7 Nikitin, Anatoly Glebovich
7 Smirnov, Roman G.
7 Suslov, Sergei K.
7 Turbiner, Alexander
7 Yasmin, Ghazala
6 Ballesteros, Angel
6 Dattoli, Giuseppe
6 del Olmo, Mariano A.
6 Marchesiello, Antonella
6 Qu, Changzheng
6 Šnobl, Libor
6 Van der Jeugt, Joris
6 Zhang, Yaozhong
5 De Bie, Hendrik
5 De Meyer, Hans E.
5 Fakhri, Hossein
5 Gaboriaud, Julien
5 Kaveh, Ali
5 Matveev, Vladimir S.
5 Ragnisco, Orlando
5 Sharp, Robert T.
5 Shirokov, Igor’ Viktorovich
5 Vanden Berghe, Guido
5 Yakhno, Alexander
4 Bagrov, Vladislav G.
4 Błaszak, Maciej
4 Bougie, Jonathan
4 Chirikjian, Gregory S.
4 Cohl, Howard Saul
4 Dobrogowska, Alina
4 Dong, Shihai
4 Enciso, Alberto
4 Gangopadhyaya, Asim
4 Healey, Timothy J.
4 Hughes, J. W. B.
4 Ishkhanyan, Artur Michaĭlovich
4 Koelink, Erik
4 Lai, Sheng-Hong
4 Lee, Jenchi
4 Liu, Zhi-Guo
4 Marciniak, Krzysztof
4 Nikbakht, Maryam
4 Obukhov, Valery V.
4 Post, Sarah
4 Rasinariu, Constantin
4 Rauch-Wojciechowski, Stefan
4 Schöbel, Konrad P.
4 Shapovalov, Aleksandr V.
4 Subag, Eyal M.
4 Torre, Amalia
4 Villalba, Víctor M.
4 Yadav, Sarasvati
4 Yang, Yi
4 Yurduşen, Ismet
4 Zassenhaus, Hans Julius
4 Zecca, Antonio
3 Calzada, Juan A.
3 Cesarano, Clemente
3 Chanu, C.
3 Chenaghlou, Alireza
3 Dwivedi, Ravi
3 El-Jaick, Léa Jaccoud
3 Faye, Grégory
3 Figueiredo, Bartolomeu D. B.
...and 874 more Authors
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Cited in 209 Serials

267 Journal of Mathematical Physics
40 Journal of Mathematical Analysis and Applications
22 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
21 Journal of Physics A: Mathematical and Theoretical
19 Physics Letters. A
19 Journal of Computational and Applied Mathematics
18 Letters in Mathematical Physics
17 Reports on Mathematical Physics
16 Theoretical and Mathematical Physics
15 Journal of Geometry and Physics
12 International Journal of Theoretical Physics
12 Applied Mathematics and Computation
12 Regular and Chaotic Dynamics
11 Journal of High Energy Physics
9 Communications in Mathematical Physics
9 Acta Applicandae Mathematicae
9 Annals of Physics
8 Computers & Mathematics with Applications
7 Linear Algebra and its Applications
7 Journal of Mathematical Sciences (New York)
7 Integral Transforms and Special Functions
7 International Journal of Geometric Methods in Modern Physics
6 Journal of Pure and Applied Algebra
6 Physica D
6 Russian Physics Journal
5 Archive for Rational Mechanics and Analysis
5 Nuclear Physics. B
5 Chaos, Solitons and Fractals
5 Advances in Mathematics
5 Studies in Applied Mathematics
5 Advances in Applied Mathematics
5 Constructive Approximation
5 The Ramanujan Journal
4 Computer Methods in Applied Mechanics and Engineering
4 General Relativity and Gravitation
4 Ukrainian Mathematical Journal
4 ZAMP. Zeitschrift für angewandte Mathematik und Physik
4 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique
4 Proceedings of the American Mathematical Society
4 Journal of Nonlinear Mathematical Physics
4 Advances in High Energy Physics
3 Modern Physics Letters A
3 Acta Mechanica
3 Computer Physics Communications
3 International Journal of Engineering Science
3 Physics Reports
3 Rocky Mountain Journal of Mathematics
3 Journal of Approximation Theory
3 Journal of Differential Equations
3 Numerische Mathematik
3 Proceedings of the Japan Academy. Series A
3 Theoretical Computer Science
3 Journal of Symbolic Computation
3 Mathematical and Computer Modelling
3 Journal of Elasticity
3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
3 Journal of Difference Equations and Applications
3 Mathematical Physics, Analysis and Geometry
3 Analysis and Applications (Singapore)
3 Nonlinear Analysis. Theory, Methods & Applications
2 International Journal of Modern Physics A
2 International Journal of Modern Physics B
2 Applicable Analysis
2 Communications in Algebra
2 Israel Journal of Mathematics
2 Journal of Applied Mathematics and Mechanics
2 Journal of Computational Physics
2 Journal of the Franklin Institute
2 Journal of Statistical Physics
2 Linear and Multilinear Algebra
2 Physics Letters. B
2 Annales de l’Institut Fourier
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 Calcolo
2 Computing
2 International Journal of Mathematics and Mathematical Sciences
2 International Journal for Numerical Methods in Engineering
2 Journal of Functional Analysis
2 Journal of Multivariate Analysis
2 Journal of Soviet Mathematics
2 Publications of the Research Institute for Mathematical Sciences, Kyoto University
2 Tohoku Mathematical Journal. Second Series
2 Japan Journal of Applied Mathematics
2 Applied Mathematics Letters
2 Differential Geometry and its Applications
2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
2 Annales de l’Institut Henri Poincaré. Physique Théorique
2 Journal of Nonlinear Science
2 Advances in Applied Clifford Algebras
2 Annals of Mathematics. Second Series
2 Acta Mathematica Sinica. English Series
2 Annales Henri Poincaré
2 Dynamical Systems
2 Mathematical Modelling of Natural Phenomena
2 Advances in Mathematical Physics
2 Acta Crystallographica. Section A
2 Communications in Applied and Industrial Mathematics
2 Mathematics
2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Archive for History of Exact Sciences
...and 109 more Serials
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Cited in 55 Fields

271 Quantum theory (81-XX)
236 Special functions (33-XX)
203 Partial differential equations (35-XX)
162 Mechanics of particles and systems (70-XX)
156 Dynamical systems and ergodic theory (37-XX)
133 Nonassociative rings and algebras (17-XX)
93 Topological groups, Lie groups (22-XX)
71 Differential geometry (53-XX)
57 Global analysis, analysis on manifolds (58-XX)
54 Ordinary differential equations (34-XX)
48 Relativity and gravitational theory (83-XX)
30 Operator theory (47-XX)
26 Numerical analysis (65-XX)
25 Difference and functional equations (39-XX)
25 Harmonic analysis on Euclidean spaces (42-XX)
23 Group theory and generalizations (20-XX)
23 Mechanics of deformable solids (74-XX)
20 Optics, electromagnetic theory (78-XX)
19 Associative rings and algebras (16-XX)
19 Statistical mechanics, structure of matter (82-XX)
17 Combinatorics (05-XX)
17 Computer science (68-XX)
15 Linear and multilinear algebra; matrix theory (15-XX)
14 Algebraic geometry (14-XX)
11 Information and communication theory, circuits (94-XX)
10 Integral transforms, operational calculus (44-XX)
9 Fluid mechanics (76-XX)
8 Functions of a complex variable (30-XX)
8 Biology and other natural sciences (92-XX)
7 Number theory (11-XX)
7 Abstract harmonic analysis (43-XX)
7 Probability theory and stochastic processes (60-XX)
6 Functional analysis (46-XX)
6 Geometry (51-XX)
6 Statistics (62-XX)
6 Systems theory; control (93-XX)
5 Commutative algebra (13-XX)
5 Approximations and expansions (41-XX)
5 Integral equations (45-XX)
4 Real functions (26-XX)
3 History and biography (01-XX)
3 Several complex variables and analytic spaces (32-XX)
3 Operations research, mathematical programming (90-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
2 Mathematical logic and foundations (03-XX)
2 Field theory and polynomials (12-XX)
2 Calculus of variations and optimal control; optimization (49-XX)
2 Convex and discrete geometry (52-XX)
1 General and overarching topics; collections (00-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 General algebraic systems (08-XX)
1 Potential theory (31-XX)
1 General topology (54-XX)
1 Algebraic topology (55-XX)
1 Manifolds and cell complexes (57-XX)

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