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Zhedanov, Alexei S.

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Author ID: zhedanov.alexei-s Recent zbMATH articles by "Zhedanov, Alexei S."
Published as: Zhedanov, A.; Zhedanov, A. S.; Zhedanov, Alexei; Zhedanov, Alexei S.; Zhedanov, Alezey
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Documents Indexed: 162 Publications since 1991

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138 Publications have been cited 1,298 times in 590 Documents Cited by Year
Rational spectral transformations and orthogonal polynomials. Zbl 0918.42016
Zhedanov, Alexei
85
1997
“Hidden symmetry” of Askey-Wilson polynomials. Zbl 0782.33012
Zhedanov, A. S.
54
1991
Mutual integrability, quadratic algebras, and dynamical symmetry. Zbl 0875.17002
Granovskij, Ya. I.; Lutzenko, I. M.; Zhedanov, A. S.
49
1992
Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum transformations. Zbl 1200.33013
Sasaki, Ryu; Tsujimoto, Satoshi; Zhedanov, Alexei
46
2010
Dunkl shift operators and Bannai-Ito polynomials. Zbl 1248.33022
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
41
2012
Discrete Darboux transformations, the discrete-time Toda lattice, and the Askey-Wilson polynomials. Zbl 0859.33017
Spiridonov, Vyacheslav; Zhedanov, Alexei
36
1995
“Hidden symmetry” of Askey-Wilson polynomials. Zbl 0744.33009
Zhedanov, A. S.
31
1991
Superintegrability in two dimensions and the Racah-Wilson algebra. Zbl 1311.81145
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
29
2014
Spectral transformation chains and some new biorthogonal rational functions. Zbl 0989.33008
Spiridonov, Vyacheslav; Zhedanov, Alexei
28
2000
Biorthogonal rational functions and the generalized eigenvalue problem. Zbl 1058.42502
Zhedanov, Alexei
28
1999
A ’missing’ family of classical orthogonal polynomials. Zbl 1222.33011
Vinet, Luc; Zhedanov, Alexei
27
2011
On some classes of polynomials orthogonal on arcs of the unit circle connected with symmetric orthogonal polynomials on an interval. Zbl 0921.42017
Zhedanov, Alexei
25
1998
A method of constructing Krall’s polynomials. Zbl 0929.33008
Zhedanov, Alexei
24
1999
The Bannai-Ito polynomials as Racah coefficients of the \(sl_{-1}(2)\) algebra. Zbl 1304.17019
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
23
2014
The Bannai-Ito algebra and a superintegrable system with reflections on the two-sphere. Zbl 1291.81132
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
21
2014
A Laplace-Dunkl equation on \(S^2\) and the Bannai-Ito algebra. Zbl 1311.22030
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
20
2015
Spectral transformations, self-similar reductions and orthogonal polynomials. Zbl 0926.39006
Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei
20
1997
The equitable Racah algebra from three \(\mathfrak {su}(1,1)\) algebras. Zbl 1355.17004
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
19
2014
The “Higgs algebra” as a “quantum” deformation of SU(2). Zbl 1021.81587
Zhedanov, A. S.
19
1992
Discrete-time Volterra chain and classical orthogonal polynomials. Zbl 0928.39007
Spiridonov, Vyacheslav; Zhedanov, Alexei
16
1997
Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra. Zbl 1351.33010
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
15
2016
A limit \(q=-1\) for the big \(q\)-Jacobi polynomials. Zbl 1276.33019
Vinet, Luc; Zhedanov, Alexei
15
2012
Tridiagonalization and the Heun equation. Zbl 1364.34126
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
14
2017
Linear covariance algebra for \(SL_ q(2)\). Zbl 0784.17019
Granovskij, Ya. I.; Zhedanov, A. S.
14
1993
The non-symmetric Wilson polynomials are the Bannai-Ito polynomials. Zbl 1354.33010
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
13
2016
The multivariate Krawtchouk polynomials as matrix elements of the rotation group representations on oscillator states. Zbl 1282.22008
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
13
2013
The Dunkl oscillator in the plane. Part I: Superintegrability, separated wavefunctions and overlap coefficients. Zbl 1267.81139
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
13
2013
Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer. Zbl 1251.81021
Vinet, Luc; Zhedanov, Alexei
13
2012
Elliptic hypergeometric Laurent biorthogonal polynomials with a dense point spectrum on the unit circle. Zbl 1163.33325
Tsujimoto, Satoshi; Zhedanov, Alexei
13
2009
The “classical” Laurent biorthogonal polynomials. Zbl 0932.33006
Zhedanov, Alexei
13
1998
Faces of relativistic Toda chain. Zbl 1089.37532
Kharchev, S.; Mironov, A.; Zhedanov, A.
13
1997
Bispectrality of the complementary Bannai-Itō polynomials. Zbl 1272.33010
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
12
2013
Automorphisms of the Heisenberg-Weyl algebra and \(d\)-orthogonal polynomials. Zbl 1202.33018
Vinet, Luc; Zhedanov, Alexei
12
2009
Difference Schrödinger operators with linear and exponential discrete spectra. Zbl 0790.33017
Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei
12
1993
Quantum spin chains with fractional revival. Zbl 1380.82030
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
11
2016
Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids. Zbl 1039.42022
Spiridonov, V. P.; Zhedanov, A. S.
11
2001
Classical biorthogonal rational functions on elliptic grids. Zbl 0974.33016
Spiridonov, Vyacheslav; Zhedanov, Alexei
11
2000
Algebraic Heun operator and band-time limiting. Zbl 1405.33025
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
10
2018
Dual \(-1\) Hahn polynomials: “classical” polynomials beyond the Leonard duality. Zbl 1300.33018
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
10
2013
A Bochner theorem for Dunkl polynomials. Zbl 1217.33022
Vinet, Luc; Zhedanov, Alexei
10
2011
An operator approach to multipoint Padé approximations. Zbl 1163.41002
Derevyagin, Maxim S.; Zhedanov, Alexei S.
10
2009
Toda chain, Stieltjes function, and orthogonal polynomials. Zbl 1121.37054
Peherstorfer, F.; Spiridonov, V. P.; Zhedanov, A. S.
10
2007
Quantum \(\text{SU}_q(2)\) algebra: “Cartesian” version and overlaps. Zbl 1020.17514
Zhedanov, A. S.
10
1992
Embeddings of the Racah algebra into the Bannai-Itô algebra. Zbl 1318.33027
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
9
2015
From \(\text{sl}_q(2)\) to a parabosonic Hopf algebra. Zbl 1246.17022
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
9
2011
The Heun operator of Hahn-type. Zbl 1429.33018
Vinet, Luc; Zhedanov, Alexei
8
2019
Supersymmetric quantum mechanics with reflections. Zbl 1230.81032
Post, Sarah; Vinet, Luc; Zhedanov, Alexei
8
2011
Representations of the Schrödinger group and matrix orthogonal polynomials. Zbl 1227.81173
Vinet, Luc; Zhedanov, Alexei
8
2011
Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials. Zbl 1136.37041
Spiridonov, V. P.; Tsujimoto, S.; Zhedanov, A. S.
8
2007
A characterization of classical and semiclassical orthogonal polynomials from their dual polynomials. Zbl 1054.33005
Vinet, Luc; Zhedanov, Alexei
8
2004
“Leonard pairs” in classical mechanics. Zbl 1039.37047
Zhedanov, Alexei; Korovnichenko, Alyona
8
2002
The quantum superalgebra \(\mathfrak{osp}_q(1| 2)\) and a \(q\)-generalization of the Bannai-Ito polynomials. Zbl 1395.17027
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
7
2016
The Dunkl oscillator in the plane. II: Representations of the symmetry algebra. Zbl 1292.81041
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
7
2014
CMV matrices and little and big \(-1\) Jacobi polynomials. Zbl 1259.42018
Derevyagin, Maxim; Vinet, Luc; Zhedanov, Alexei
7
2012
\(d\)-orthogonal polynomials and \(\mathfrak {su}(2)\). Zbl 1238.33004
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
7
2012
Special solutions of the Toda chain and combinatorial numbers. Zbl 1050.37039
Nakamura, Yoshimasa; Zhedanov, Alexei
7
2004
Szegő polynomials on the real axis. Zbl 0939.33010
Vinet, Luc; Zhedanov, Alexei
7
1999
On the polynomials orthogonal on regular polygons. Zbl 0932.33002
Zhedanov, Alexei
7
1999
Zeros and orthogonality of the Askey-Wilson polynomials for \(q\) a root of unity. Zbl 0882.33007
Spiridonov, Vyacheslav; Zhedanov, Alexei
7
1997
New construction of \(3nj\)-symbols. Zbl 0856.22031
Granovskij, Ya. I.; Zhedanov, A. S.
7
1993
The Racah algebra as a commutant and Howe duality. Zbl 1411.81112
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei
6
2018
Tridiagonal representations of the \(q\)-oscillator algebra and Askey-Wilson polynomials. Zbl 1368.81074
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
6
2017
Quasi-linear algebras and integrability (the Heisenberg picture). Zbl 1136.17019
Vinet, Luc; Zhedanov, Alexei
6
2008
Spectral transformations and generalized Pollaczek polynomials. Zbl 0956.33006
Yermolayeva, Oksana; Zhedanov, Alexei
6
1999
The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type. Zbl 1423.33027
Baseilhac, Pascal; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
5
2019
An embedding of the Bannai-Ito algebra in \(\mathcal U(\mathfrak{osp}(1,2))\) and \(-1\) polynomials. Zbl 1395.81126
Baseilhac, Pascal; Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
5
2018
Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials. Zbl 1375.65059
Genest, Vincent X.; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
5
2017
The para-Racah polynomials. Zbl 1333.33025
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
5
2016
Bannai-Ito polynomials and dressing chains. Zbl 1304.42063
Derevyagin, Maxim; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
5
2014
The algebra of dual \(-1\) Hahn polynomials and the Clebsch-Gordan problem of \(\mathfrak{sl}_{-1}(2)\). Zbl 1280.81071
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
5
2013
An algebraic model for the multiple Meixner polynomials of the first kind. Zbl 1251.81053
Miki, Hiroshi; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
5
2012
The linear pencil approach to rational interpolation. Zbl 1193.41001
Beckermann, Bernhard; Derevyagin, Maxim; Zhedanov, Alexei
5
2010
“Leonard pairs” in classical mechanics. Zbl 1034.37031
Zhedanov, A.; Korovnichenko, A.
5
2002
Generalized little \(q\)-Jacobi polynomials as eigensolutions of higher-order \(q\)-difference operators. Zbl 0973.33009
Vinet, Luc; Zhedanov, Alexei
5
2001
Self-similarity, spectral transformations and orthogonal and biorthogonal polynomials. Zbl 1010.42014
Spiridonov, Vyacheslav; Zhedanov, Alexei
5
1999
An integrable chain and bi-orthogonal polynomials. Zbl 0957.37055
Vinet, Luc; Zhedanov, Alexei
5
1998
\(9j\)-symbols of the oscillator algebra and Krawtchouk polynomials in two variables. Zbl 0952.33010
Zhedanov, Alexei
5
1997
\(q\) rotations and other \(q\) transformations as unitary nonlinear automorphisms of quantum algebras. Zbl 0789.17011
Zhedanov, A. S.
5
1993
‘Twisted’ Clebsch-Gordan coefficients for \(SU_ q(2)\). Zbl 0765.17015
Granovskij, Ya. I.; Zhedanov, A. S.
5
1992
Nonlinear shift \(q\)-Bose operators and \(q\)-coherent states. Zbl 0757.33007
Zhedanov, A. S.
5
1991
The q-Heun operator of big q-Jacobi type and the q-Heun algebra. Zbl 1444.39007
Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei
4
2020
The dual pair \(Pin(2n) \times \mathfrak{osp}(1|2)\), the Dirac equation and the Bannai-Ito algebra. Zbl 1402.81132
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei
4
2018
A \(q\)-generalization of the para-Racah polynomials. Zbl 1390.33035
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
4
2018
An analytic spin chain model with fractional revival. Zbl 1351.82044
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
4
2016
\(q\)-rotations and Krawtchouk polynomials. Zbl 1339.33020
Genest, Vincent X.; Post, Sarah; Vinet, Luc; Yu, Guo-Fu; Zhedanov, Alexei
4
2016
The multivariate Charlier polynomials as matrix elements of the Euclidean group representation on oscillator states. Zbl 1296.33025
Genest, Vincent X.; Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei
4
2014
A “continuous” limit of the complementary Bannai-Itô polynomials: Chihara polynomials. Zbl 1293.33012
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
4
2014
The singular and the 2:1 anisotropic Dunkl oscillators in the plane. Zbl 1273.81089
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
4
2013
Jordan algebras and orthogonal polynomials. Zbl 1272.17031
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
4
2011
Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials. Zbl 1255.81143
Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei
4
2011
Two-dimensional Krall-Sheffer polynomials and quantum systems on spaces with constant curvature. Zbl 1031.33009
Vinet, Luc; Zhedanov, Alexei
4
2003
Spectral transformations of the Laurent biorthogonal polynomials. II: Pastro polynomials. Zbl 1065.33011
Vinet, Luc; Zhedanov, Alexei
4
2001
Bispectrality and Darboux transformations in the theory of orthogonal polynomials. Zbl 0901.42015
Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei
4
1998
Discrete reflectionless potentials, quantum algebras, and \(q\)-orthogonal polynomials. Zbl 0813.35098
Spiridonov, Vyacheslav; Zhedanov, Alexei
4
1995
Spherical \(q\)-functions. Zbl 0854.33013
Granovskij, Ya. I.; Zhedanov, A. S.
4
1993
Exact state revival in a spin chain with next-to-nearest neighbour interactions. Zbl 1390.82011
Christandl, Matthias; Vinet, Luc; Zhedanov, Alexei
3
2017
The equitable presentation of \(\mathfrak{osp}_q(1|2)\) and a \(q\)-analog of the Bannai-Ito algebra. Zbl 1344.17014
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
3
2015
The multivariate Meixner polynomials as matrix elements of \(SO(d, 1)\) representations on oscillator states. Zbl 1285.81023
Genest, Vincent X.; Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei
3
2014
Interbasis expansions for the isotropic 3D harmonic oscillator and bivariate Krawtchouk polynomials. Zbl 1283.81064
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
3
2014
Birth and death processes and quantum spin chains. Zbl 1285.82028
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
3
2013
The q-Heun operator of big q-Jacobi type and the q-Heun algebra. Zbl 1444.39007
Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei
4
2020
Signal processing, orthogonal polynomials, and Heun equations. Zbl 1443.33033
Bergeron, Geoffroy; Vinet, Luc; Zhedanov, Alexei
2
2020
Heun algebras of Lie type. Zbl 1452.17024
Crampé, Nicolas; Vinet, Luc; Zhedanov, Alexei
2
2020
The Heun-Racah and Heun-Bannai-Ito algebras. Zbl 07287189
Bergeron, Geoffroy; Crampé, Nicolas; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
1
2020
Little and big \(q\)-Jacobi polynomials and the Askey-Wilson algebra. Zbl 1436.81070
Baseilhac, Pascal; Martin, Xavier; Vinet, Luc; Zhedanov, Alexei
1
2020
The Heun operator of Hahn-type. Zbl 1429.33018
Vinet, Luc; Zhedanov, Alexei
8
2019
The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type. Zbl 1423.33027
Baseilhac, Pascal; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
5
2019
Algebraic Heun operator and band-time limiting. Zbl 1405.33025
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
10
2018
The Racah algebra as a commutant and Howe duality. Zbl 1411.81112
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei
6
2018
An embedding of the Bannai-Ito algebra in \(\mathcal U(\mathfrak{osp}(1,2))\) and \(-1\) polynomials. Zbl 1395.81126
Baseilhac, Pascal; Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
5
2018
The dual pair \(Pin(2n) \times \mathfrak{osp}(1|2)\), the Dirac equation and the Bannai-Ito algebra. Zbl 1402.81132
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei
4
2018
A \(q\)-generalization of the para-Racah polynomials. Zbl 1390.33035
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
4
2018
Tridiagonalization and the Heun equation. Zbl 1364.34126
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
14
2017
Tridiagonal representations of the \(q\)-oscillator algebra and Askey-Wilson polynomials. Zbl 1368.81074
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
6
2017
Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials. Zbl 1375.65059
Genest, Vincent X.; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
5
2017
Exact state revival in a spin chain with next-to-nearest neighbour interactions. Zbl 1390.82011
Christandl, Matthias; Vinet, Luc; Zhedanov, Alexei
3
2017
The \(q\)-Onsager algebra and multivariable \(q\)-special functions. Zbl 1375.81138
Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei
2
2017
Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra. Zbl 1351.33010
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
15
2016
The non-symmetric Wilson polynomials are the Bannai-Ito polynomials. Zbl 1354.33010
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
13
2016
Quantum spin chains with fractional revival. Zbl 1380.82030
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
11
2016
The quantum superalgebra \(\mathfrak{osp}_q(1| 2)\) and a \(q\)-generalization of the Bannai-Ito polynomials. Zbl 1395.17027
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
7
2016
The para-Racah polynomials. Zbl 1333.33025
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
5
2016
An analytic spin chain model with fractional revival. Zbl 1351.82044
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
4
2016
\(q\)-rotations and Krawtchouk polynomials. Zbl 1339.33020
Genest, Vincent X.; Post, Sarah; Vinet, Luc; Yu, Guo-Fu; Zhedanov, Alexei
4
2016
Hypergeometric orthogonal polynomials with respect to Newtonian bases. Zbl 1341.42045
Vinet, Luc; Zhedanov, Alexei
2
2016
A Laplace-Dunkl equation on \(S^2\) and the Bannai-Ito algebra. Zbl 1311.22030
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
20
2015
Embeddings of the Racah algebra into the Bannai-Itô algebra. Zbl 1318.33027
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
9
2015
The equitable presentation of \(\mathfrak{osp}_q(1|2)\) and a \(q\)-analog of the Bannai-Ito algebra. Zbl 1344.17014
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
3
2015
Two-variable -1 Jacobi polynomials. Zbl 1317.33011
Genest, Vincent X.; Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
1
2015
Superintegrability in two dimensions and the Racah-Wilson algebra. Zbl 1311.81145
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
29
2014
The Bannai-Ito polynomials as Racah coefficients of the \(sl_{-1}(2)\) algebra. Zbl 1304.17019
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
23
2014
The Bannai-Ito algebra and a superintegrable system with reflections on the two-sphere. Zbl 1291.81132
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
21
2014
The equitable Racah algebra from three \(\mathfrak {su}(1,1)\) algebras. Zbl 1355.17004
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
19
2014
The Dunkl oscillator in the plane. II: Representations of the symmetry algebra. Zbl 1292.81041
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
7
2014
Bannai-Ito polynomials and dressing chains. Zbl 1304.42063
Derevyagin, Maxim; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
5
2014
The multivariate Charlier polynomials as matrix elements of the Euclidean group representation on oscillator states. Zbl 1296.33025
Genest, Vincent X.; Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei
4
2014
A “continuous” limit of the complementary Bannai-Itô polynomials: Chihara polynomials. Zbl 1293.33012
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
4
2014
The multivariate Meixner polynomials as matrix elements of \(SO(d, 1)\) representations on oscillator states. Zbl 1285.81023
Genest, Vincent X.; Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei
3
2014
Interbasis expansions for the isotropic 3D harmonic oscillator and bivariate Krawtchouk polynomials. Zbl 1283.81064
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
3
2014
Elliptic solutions of the Toda chain and a generalization of the Stieltjes-Carlitz polynomials. Zbl 1298.33020
Zhedanov, Alexei
1
2014
Umbral “classical” polynomials. Zbl 1305.33024
Zhedanov, Alexei
1
2014
The multivariate Krawtchouk polynomials as matrix elements of the rotation group representations on oscillator states. Zbl 1282.22008
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
13
2013
The Dunkl oscillator in the plane. Part I: Superintegrability, separated wavefunctions and overlap coefficients. Zbl 1267.81139
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
13
2013
Bispectrality of the complementary Bannai-Itō polynomials. Zbl 1272.33010
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
12
2013
Dual \(-1\) Hahn polynomials: “classical” polynomials beyond the Leonard duality. Zbl 1300.33018
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
10
2013
The algebra of dual \(-1\) Hahn polynomials and the Clebsch-Gordan problem of \(\mathfrak{sl}_{-1}(2)\). Zbl 1280.81071
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
5
2013
The singular and the 2:1 anisotropic Dunkl oscillators in the plane. Zbl 1273.81089
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
4
2013
Birth and death processes and quantum spin chains. Zbl 1285.82028
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
3
2013
A superintegrable finite oscillator in two dimensions with \(SU(2)\) symmetry. Zbl 1266.39011
Miki, Hiroshi; Post, Sarah; Vinet, Luc; Zhedanov, Alexei
3
2013
On Dirichlet, Poncelet and Abel problems. Zbl 1264.14043
Burskii, Vladimir P.; Zhedanov, Alexei S.
3
2013
The Hahn superalgebra and supersymmetric Dunkl oscillator models. Zbl 1280.81060
Genest, Vincent X.; Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
2
2013
Dunkl shift operators and Bannai-Ito polynomials. Zbl 1248.33022
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
41
2012
A limit \(q=-1\) for the big \(q\)-Jacobi polynomials. Zbl 1276.33019
Vinet, Luc; Zhedanov, Alexei
15
2012
Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer. Zbl 1251.81021
Vinet, Luc; Zhedanov, Alexei
13
2012
CMV matrices and little and big \(-1\) Jacobi polynomials. Zbl 1259.42018
Derevyagin, Maxim; Vinet, Luc; Zhedanov, Alexei
7
2012
\(d\)-orthogonal polynomials and \(\mathfrak {su}(2)\). Zbl 1238.33004
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
7
2012
An algebraic model for the multiple Meixner polynomials of the first kind. Zbl 1251.81053
Miki, Hiroshi; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
5
2012
Generalized squeezed-coherent states of the finite one-dimensional oscillator and matrix multi-orthogonality. Zbl 1247.81197
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
1
2012
A ’missing’ family of classical orthogonal polynomials. Zbl 1222.33011
Vinet, Luc; Zhedanov, Alexei
27
2011
A Bochner theorem for Dunkl polynomials. Zbl 1217.33022
Vinet, Luc; Zhedanov, Alexei
10
2011
From \(\text{sl}_q(2)\) to a parabosonic Hopf algebra. Zbl 1246.17022
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
9
2011
Supersymmetric quantum mechanics with reflections. Zbl 1230.81032
Post, Sarah; Vinet, Luc; Zhedanov, Alexei
8
2011
Representations of the Schrödinger group and matrix orthogonal polynomials. Zbl 1227.81173
Vinet, Luc; Zhedanov, Alexei
8
2011
Jordan algebras and orthogonal polynomials. Zbl 1272.17031
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
4
2011
Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials. Zbl 1255.81143
Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei
4
2011
An infinite family of superintegrable Hamiltonians with reflection in the plane. Zbl 1238.81138
Post, Sarah; Vinet, Luc; Zhedanov, Alexei
1
2011
Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum transformations. Zbl 1200.33013
Sasaki, Ryu; Tsujimoto, Satoshi; Zhedanov, Alexei
46
2010
The linear pencil approach to rational interpolation. Zbl 1193.41001
Beckermann, Bernhard; Derevyagin, Maxim; Zhedanov, Alexei
5
2010
Elliptic hypergeometric Laurent biorthogonal polynomials with a dense point spectrum on the unit circle. Zbl 1163.33325
Tsujimoto, Satoshi; Zhedanov, Alexei
13
2009
Automorphisms of the Heisenberg-Weyl algebra and \(d\)-orthogonal polynomials. Zbl 1202.33018
Vinet, Luc; Zhedanov, Alexei
12
2009
An operator approach to multipoint Padé approximations. Zbl 1163.41002
Derevyagin, Maxim S.; Zhedanov, Alexei S.
10
2009
Elliptic polynomials orthogonal on the unit circle with a dense point spectrum. Zbl 1178.33022
Zhedanov, Alexei
3
2009
Elliptic solutions of the restricted Toda chain, Lamé polynomials and generalization of the elliptic Stieltjes polynomials. Zbl 1179.33035
Vinet, Luc; Zhedanov, Alexei
1
2009
Quasi-linear algebras and integrability (the Heisenberg picture). Zbl 1136.17019
Vinet, Luc; Zhedanov, Alexei
6
2008
Generalized Bochner theorem: Characterization of the Askey-Wilson polynomials. Zbl 1140.33006
Vinet, Luc; Zhedanov, Alexei
3
2008
Toda chain, Stieltjes function, and orthogonal polynomials. Zbl 1121.37054
Peherstorfer, F.; Spiridonov, V. P.; Zhedanov, A. S.
10
2007
Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials. Zbl 1136.37041
Spiridonov, V. P.; Tsujimoto, S.; Zhedanov, A. S.
8
2007
Elliptic grids, rational functions, and the Padé interpolation. Zbl 1136.42021
Spiridonov, V. P.; Zhedanov, A. S.
3
2007
On Dirichlet problem for string equation, Poncelet problem, Pell-Abel equation, and some other related problems. Zbl 1120.35061
Burskij, V. P.; Zhedanov, A. S.
3
2006
Dirichlet and Neumann problems for string equation, Poncelet problem and Pell-Abel equation. Zbl 1092.35054
Burskii, Vladimir P.; Zhedanov, Alexei S.
1
2006
Regular algebras of dimension 2, the generalized eigenvalue problem and Padé interpolation. Zbl 1126.39017
Zhedanov, Alexei
2
2005
Explicit multipoint rational interpolation Padé table for exponential and power functions. Zbl 1122.41008
Zhedanov, A.
1
2005
A characterization of classical and semiclassical orthogonal polynomials from their dual polynomials. Zbl 1054.33005
Vinet, Luc; Zhedanov, Alexei
8
2004
Special solutions of the Toda chain and combinatorial numbers. Zbl 1050.37039
Nakamura, Yoshimasa; Zhedanov, Alexei
7
2004
Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials. Zbl 1071.33013
Grünbaum, F. A.; Vinet, Luc; Zhedanov, Alexei
2
2004
Toda chain, Sheffer class of orthogonal polynomials and combinatorial numbers. Zbl 1095.37030
Nakamura, Y.; Zhedanov, A.
1
2004
Biorthogonality of the Lagrange interpolants. Zbl 1065.41009
Zhedanov, Alexei
1
2004
Two-dimensional Krall-Sheffer polynomials and quantum systems on spaces with constant curvature. Zbl 1031.33009
Vinet, Luc; Zhedanov, Alexei
4
2003
“Leonard pairs” in classical mechanics. Zbl 1039.37047
Zhedanov, Alexei; Korovnichenko, Alyona
8
2002
“Leonard pairs” in classical mechanics. Zbl 1034.37031
Zhedanov, A.; Korovnichenko, A.
5
2002
Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids. Zbl 1039.42022
Spiridonov, V. P.; Zhedanov, A. S.
11
2001
Generalized little \(q\)-Jacobi polynomials as eigensolutions of higher-order \(q\)-difference operators. Zbl 0973.33009
Vinet, Luc; Zhedanov, Alexei
5
2001
Spectral transformations of the Laurent biorthogonal polynomials. II: Pastro polynomials. Zbl 1065.33011
Vinet, Luc; Zhedanov, Alexei
4
2001
Two-dimensional Krall-Sheffer polynomials and integrable systems. Zbl 0995.33009
Harnad, John; Vinet, Luc; Yermolayeva, Oksana; Zhedanov, Alexei
3
2001
A method to study the Krall and \(q\)-Krall polynomials. Zbl 0990.33011
Vinet, Luc; Yermolayeva, Oksana; Zhedanov, Alexei
3
2001
Spectral transformations of the Laurent biorthogonal polynomials. I: \(q\)-Appel polynomials. Zbl 1064.33017
Vinet, Luc; Zhedanov, Alexei
2
2001
Dual algebras with nonlinear Poisson brackets. Zbl 1008.17014
Korovnichenko, A.; Zhedanov, A.
1
2001
Spectral transformation chains and some new biorthogonal rational functions. Zbl 0989.33008
Spiridonov, Vyacheslav; Zhedanov, Alexei
28
2000
Classical biorthogonal rational functions on elliptic grids. Zbl 0974.33016
Spiridonov, Vyacheslav; Zhedanov, Alexei
11
2000
Biorthogonal rational functions and the generalized eigenvalue problem. Zbl 1058.42502
Zhedanov, Alexei
28
1999
...and 38 more Documents
all top 5

Cited by 506 Authors

80 Vinet, Luc
71 Zhedanov, Alexei S.
36 Marcellán Español, Francisco
24 Genest, Vincent X.
24 Terwilliger, Paul M.
20 Duran, Antonio J.
20 Ranga, A. Sri
18 Tsujimoto, Satoshi
15 Spiridonov, Vyacheslav Pavlovich
13 Derevyagin, Maxim S.
11 Garza, Luis E.
11 Nomura, Kazumasa
10 Baseilhac, Pascal
10 Bracciali, Cleonice F.
10 Castillo, Kenier
10 Huang, Hau-wen
10 Odake, Satoru
9 De Bie, Hendrik
9 Iliev, Plamen
9 Jordaan, Kerstin
8 Crampé, Nicolas
8 Gaboriaud, Julien
8 García-Ardila, Juan Carlos
7 Alhaidari, Abdulaziz D.
7 Ito, Tatsuro
7 Pérez, Teresa E.
7 Quesne, Christiane
7 Sri Ranga, Alagacone
7 Van der Jeugt, Joris
6 Chang, Xiangke
6 Chung, Won-Sang
6 Domínguez de la Iglesia, Manuel
6 Driver, Kathy A.
6 Hu, Xingbiao
6 Ismail, Mourad El-Houssieny
6 Iwasaki, Masashi
6 Lemay, Jean-Michel
6 Rebocho, M. N.
6 Van Assche, Walter
5 Area, Iván
5 Bergeron, Geoffroy
5 Bouzeffour, Fethi
5 Godoy, Eduardo Paciência
5 Gómez-Ullate, David
5 Grandati, Yves
5 Grünbaum, Francisco Alberto
5 Marquette, Ian
5 Miki, Hiroshi
5 Milson, Robert
5 Nakamura, Yoshimasa
5 Piñar, Miguel A.
5 Rains, Eric M.
5 Roy, Barnana
5 Sasaki, Ryu
5 van de Vijver, Wouter
5 Veronese, Daniel O.
4 Alfaro García, Manuel
4 Álvarez-Nodarse, Renato
4 Bockting-Conrad, Sarah
4 Branquinho, Amílcar José Pinto Lopes
4 Filipuk, Galina V.
4 Gao, Suogang
4 Hernández, Javier
4 Hou, Bo
4 Huertas Cejudo, Edmundo José
4 Kwon, Kil Hyun
4 Lamblém, Regina Litz
4 Marriaga, Misael E.
4 Peña, Ana
4 Rezola, María Luisa
4 Rosengren, Hjalmar
4 Tamon, Christino
4 Warnaar, S. Ole
4 Yu, Guofu
4 Zagorodnyuk, Sergey Mihaylovich
4 Zhan, Hanmeng
3 Behera, Kiran Kumar
3 Bihun, Oksana
3 Bueno, María Isabel
3 Cantero, María José
3 Chan, Ada
3 Choque Rivero, Abdon Eddy
3 Costas-Santos, Roberto S.
3 Coutinho, Gabriel
3 de Andrade, Eliana X. L.
3 Garza, Lino G.
3 Griffiths, Robert C.
3 Hassanabadi, Hassan
3 He, Yi
3 Ho, Choon-Lin
3 Horozov, Emil Ivanov
3 Koelink, Erik
3 Li, Shihao
3 Magnus, Alphonse Ph.
3 McCabe, John H.
3 Moral, Leandro
3 Ndayiragije, François
3 Oste, Roy
3 Post, Sarah
3 Rafaeli, Fernando Rodrigo
...and 406 more Authors
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Cited in 125 Serials

66 Journal of Mathematical Physics
45 Journal of Approximation Theory
36 Linear Algebra and its Applications
32 Journal of Mathematical Analysis and Applications
29 Journal of Computational and Applied Mathematics
19 Proceedings of the American Mathematical Society
17 Integral Transforms and Special Functions
17 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
16 Letters in Mathematical Physics
12 Communications in Mathematical Physics
12 The Ramanujan Journal
11 Nuclear Physics. B
11 Applied Mathematics and Computation
10 Physics Letters. A
10 Journal of Physics A: Mathematical and Theoretical
9 Advances in Mathematics
9 Constructive Approximation
8 Numerical Algorithms
7 Theoretical and Mathematical Physics
7 Journal of Difference Equations and Applications
6 Journal of High Energy Physics
5 Modern Physics Letters A
5 Rocky Mountain Journal of Mathematics
5 Mathematics of Computation
5 Journal of Algebra
5 Acta Applicandae Mathematicae
5 Annals of Physics
4 International Journal of Modern Physics A
4 Communications in Algebra
4 International Journal of Theoretical Physics
4 Transactions of the American Mathematical Society
4 Applied Numerical Mathematics
4 Indagationes Mathematicae. New Series
4 Journal of Mathematical Sciences (New York)
4 St. Petersburg Mathematical Journal
3 Duke Mathematical Journal
3 Journal of Combinatorial Theory. Series A
3 Annales Henri Poincaré
3 Journal of Nonlinear Mathematical Physics
3 Computational Methods and Function Theory
3 Journal of Algebra and its Applications
2 Applicable Analysis
2 Computers & Mathematics with Applications
2 Discrete Mathematics
2 Journal d’Analyse Mathématique
2 Journal of Statistical Physics
2 Linear and Multilinear Algebra
2 Reports on Mathematical Physics
2 Calcolo
2 Journal of Differential Equations
2 Journal of Functional Analysis
2 Journal of Statistical Planning and Inference
2 Russian Mathematics
2 Journal of Algebraic Combinatorics
2 Computational and Applied Mathematics
2 Selecta Mathematica. New Series
2 Regular and Chaotic Dynamics
2 Journal of Modern Optics
2 Journal of Systems Science and Complexity
2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
2 International Journal of Geometric Methods in Modern Physics
2 Mediterranean Journal of Mathematics
2 Analysis and Mathematical Physics
1 International Journal of Modern Physics B
1 Discrete Applied Mathematics
1 Journal of Engineering Mathematics
1 Nonlinearity
1 Physica A
1 Ukrainian Mathematical Journal
1 Journal of Geometry and Physics
1 Annales de l’Institut Fourier
1 Colloquium Mathematicum
1 Journal of Applied Probability
1 Journal of Number Theory
1 Mathematische Nachrichten
1 Nagoya Mathematical Journal
1 Numerische Mathematik
1 Results in Mathematics
1 Studies in Applied Mathematics
1 Annals of Global Analysis and Geometry
1 Physica D
1 SIAM Journal on Discrete Mathematics
1 SIAM Journal on Matrix Analysis and Applications
1 Sugaku Expositions
1 International Journal of Mathematics
1 Japan Journal of Industrial and Applied Mathematics
1 Designs, Codes and Cryptography
1 Applied Mathematical Modelling
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Expositiones Mathematicae
1 Experimental Mathematics
1 International Journal of Modern Physics D
1 Georgian Mathematical Journal
1 Advances in Applied Clifford Algebras
1 The Electronic Journal of Combinatorics
1 Discussiones Mathematicae. Graph Theory
1 Sbornik: Mathematics
1 ELA. The Electronic Journal of Linear Algebra
1 Journal of Mathematical Chemistry
1 Séminaire Lotharingien de Combinatoire
...and 25 more Serials
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Cited in 47 Fields

349 Special functions (33-XX)
182 Harmonic analysis on Euclidean spaces (42-XX)
165 Quantum theory (81-XX)
79 Nonassociative rings and algebras (17-XX)
60 Linear and multilinear algebra; matrix theory (15-XX)
58 Dynamical systems and ergodic theory (37-XX)
49 Combinatorics (05-XX)
45 Ordinary differential equations (34-XX)
41 Operator theory (47-XX)
40 Difference and functional equations (39-XX)
27 Numerical analysis (65-XX)
26 Partial differential equations (35-XX)
24 Functions of a complex variable (30-XX)
23 Approximations and expansions (41-XX)
21 Associative rings and algebras (16-XX)
21 Topological groups, Lie groups (22-XX)
15 Statistical mechanics, structure of matter (82-XX)
13 Group theory and generalizations (20-XX)
13 Mechanics of particles and systems (70-XX)
12 Probability theory and stochastic processes (60-XX)
9 Number theory (11-XX)
8 Algebraic geometry (14-XX)
7 Real functions (26-XX)
7 Global analysis, analysis on manifolds (58-XX)
5 Functional analysis (46-XX)
5 Differential geometry (53-XX)
5 Relativity and gravitational theory (83-XX)
3 Commutative algebra (13-XX)
3 Statistics (62-XX)
2 General algebraic systems (08-XX)
2 Measure and integration (28-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Sequences, series, summability (40-XX)
2 Integral equations (45-XX)
2 Geometry (51-XX)
2 Biology and other natural sciences (92-XX)
2 Information and communication theory, circuits (94-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Field theory and polynomials (12-XX)
1 Potential theory (31-XX)
1 Abstract harmonic analysis (43-XX)
1 Integral transforms, operational calculus (44-XX)
1 Convex and discrete geometry (52-XX)
1 Manifolds and cell complexes (57-XX)
1 Computer science (68-XX)
1 Optics, electromagnetic theory (78-XX)
1 Systems theory; control (93-XX)

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