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Zhedanov, Alexei S.

Author ID: zhedanov.alexei-s Recent zbMATH articles by "Zhedanov, Alexei S."
Published as: Zhedanov, Alexei; Zhedanov, A. S.; Zhedanov, A.; Zhedanov, Alexei S.; Zhedanov, Alezey
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Publications by Year

Citations contained in zbMATH Open

154 Publications have been cited 1,948 times in 822 Documents Cited by Year
Rational spectral transformations and orthogonal polynomials. Zbl 0918.42016
Zhedanov, Alexei
111
1997
“Hidden symmetry” of Askey-Wilson polynomials. Zbl 0782.33012
Zhedanov, A. S.
91
1991
Mutual integrability, quadratic algebras, and dynamical symmetry. Zbl 0875.17002
Granovskij, Ya. I.; Lutzenko, I. M.; Zhedanov, A. S.
63
1992
Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum transformations. Zbl 1200.33013
Sasaki, Ryu; Tsujimoto, Satoshi; Zhedanov, Alexei
62
2010
Dunkl shift operators and Bannai-Ito polynomials. Zbl 1248.33022
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
58
2012
Superintegrability in two dimensions and the Racah-Wilson algebra. Zbl 1311.81145
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
55
2014
Discrete Darboux transformations, the discrete-time Toda lattice, and the Askey-Wilson polynomials. Zbl 0859.33017
Spiridonov, Vyacheslav; Zhedanov, Alexei
43
1995
Biorthogonal rational functions and the generalized eigenvalue problem. Zbl 1058.42502
Zhedanov, Alexei
39
1999
Spectral transformation chains and some new biorthogonal rational functions. Zbl 0989.33008
Spiridonov, Vyacheslav; Zhedanov, Alexei
38
2000
A ’missing’ family of classical orthogonal polynomials. Zbl 1222.33011
Vinet, Luc; Zhedanov, Alexei
36
2011
Algebraic Heun operator and band-time limiting. Zbl 1405.33025
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
34
2018
“Hidden symmetry” of Askey-Wilson polynomials. Zbl 0744.33009
Zhedanov, A. S.
32
1991
The Bannai-Ito polynomials as Racah coefficients of the \(sl_{-1}(2)\) algebra. Zbl 1304.17019
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
31
2014
A method of constructing Krall’s polynomials. Zbl 0929.33008
Zhedanov, Alexei
30
1999
The Bannai-Ito algebra and a superintegrable system with reflections on the two-sphere. Zbl 1291.81132
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
29
2014
Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer. Zbl 1251.81021
Vinet, Luc; Zhedanov, Alexei
28
2012
The equitable Racah algebra from three \(\mathfrak {su}(1,1)\) algebras. Zbl 1355.17004
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
28
2014
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
28
2013
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
27
1998
Tridiagonalization and the Heun equation. Zbl 1364.34126
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
25
2017
A limit \(q=-1\) for the big \(q\)-Jacobi polynomials. Zbl 1276.33019
Vinet, Luc; Zhedanov, Alexei
25
2012
Discrete-time Volterra chain and classical orthogonal polynomials. Zbl 0928.39007
Spiridonov, Vyacheslav; Zhedanov, Alexei
24
1997
A Laplace-Dunkl equation on \(S^2\) and the Bannai-Ito algebra. Zbl 1311.22030
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
24
2015
Faces of relativistic Toda chain. Zbl 1089.37532
Kharchev, S.; Mironov, A.; Zhedanov, A.
23
1997
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
23
2014
Linear covariance algebra for \(SL_ q(2)\). Zbl 0784.17019
Granovskij, Ya. I.; Zhedanov, A. S.
22
1993
The “Higgs algebra” as a “quantum” deformation of SU(2). Zbl 1021.81587
Zhedanov, A. S.
22
1992
Quantum spin chains with fractional revival. Zbl 1380.82030
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
21
2016
Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra. Zbl 1351.33010
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
21
2016
Spectral transformations, self-similar reductions and orthogonal polynomials. Zbl 0926.39006
Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei
20
1997
The “classical” Laurent biorthogonal polynomials. Zbl 0932.33006
Zhedanov, Alexei
20
1998
Toda chain, Stieltjes function, and orthogonal polynomials. Zbl 1121.37054
Peherstorfer, F.; Spiridonov, V. P.; Zhedanov, A. S.
18
2007
The non-symmetric Wilson polynomials are the Bannai-Ito polynomials. Zbl 1354.33010
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
18
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
18
2013
The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type. Zbl 1423.33027
Baseilhac, Pascal; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
18
2019
Embeddings of the Racah algebra into the Bannai-Itô algebra. Zbl 1318.33027
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
17
2015
The Heun operator of Hahn-type. Zbl 1429.33018
Vinet, Luc; Zhedanov, Alexei
17
2019
Elliptic hypergeometric Laurent biorthogonal polynomials with a dense point spectrum on the unit circle. Zbl 1163.33325
Tsujimoto, Satoshi; Zhedanov, Alexei
16
2009
Automorphisms of the Heisenberg-Weyl algebra and \(d\)-orthogonal polynomials. Zbl 1202.33018
Vinet, Luc; Zhedanov, Alexei
16
2009
From \(\text{sl}_q(2)\) to a parabosonic Hopf algebra. Zbl 1246.17022
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
15
2011
The Racah algebra as a commutant and Howe duality. Zbl 1411.81112
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei
15
2018
Bispectrality of the complementary Bannai-Itō polynomials. Zbl 1272.33010
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
15
2013
Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials. Zbl 1136.37041
Spiridonov, V. P.; Tsujimoto, S.; Zhedanov, A. S.
14
2007
Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids. Zbl 1039.42022
Spiridonov, V. P.; Zhedanov, A. S.
14
2001
A characterization of classical and semiclassical orthogonal polynomials from their dual polynomials. Zbl 1054.33005
Vinet, Luc; Zhedanov, Alexei
14
2004
The q-Heun operator of big q-Jacobi type and the q-Heun algebra. Zbl 1444.39007
Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei
14
2020
Classical biorthogonal rational functions on elliptic grids. Zbl 0974.33016
Spiridonov, Vyacheslav; Zhedanov, Alexei
13
2000
Supersymmetric quantum mechanics with reflections. Zbl 1230.81032
Post, Sarah; Vinet, Luc; Zhedanov, Alexei
13
2011
Difference Schrödinger operators with linear and exponential discrete spectra. Zbl 0790.33017
Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei
13
1993
Dual \(-1\) Hahn polynomials: “classical” polynomials beyond the Leonard duality. Zbl 1300.33018
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
13
2013
An operator approach to multipoint Padé approximations. Zbl 1163.41002
Derevyagin, Maxim S.; Zhedanov, Alexei S.
12
2009
Heun algebras of Lie type. Zbl 1452.17024
Crampé, Nicolas; Vinet, Luc; Zhedanov, Alexei
11
2020
The singular and the 2:1 anisotropic Dunkl oscillators in the plane. Zbl 1273.81089
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
11
2013
Quantum \(\text{SU}_q(2)\) algebra: “Cartesian” version and overlaps. Zbl 1020.17514
Zhedanov, A. S.
10
1992
An integrable chain and bi-orthogonal polynomials. Zbl 0957.37055
Vinet, Luc; Zhedanov, Alexei
10
1998
Special solutions of the Toda chain and combinatorial numbers. Zbl 1050.37039
Nakamura, Yoshimasa; Zhedanov, Alexei
10
2004
A Bochner theorem for Dunkl polynomials. Zbl 1217.33022
Vinet, Luc; Zhedanov, Alexei
10
2011
Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials. Zbl 1375.65059
Genest, Vincent X.; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
10
2017
The para-Racah polynomials. Zbl 1333.33025
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
10
2016
The linear pencil approach to rational interpolation. Zbl 1193.41001
Beckermann, Bernhard; Derevyagin, Maxim; Zhedanov, Alexei
9
2010
\(d\)-orthogonal polynomials and \(\mathfrak {su}(2)\). Zbl 1238.33004
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
9
2012
On the polynomials orthogonal on regular polygons. Zbl 0932.33002
Zhedanov, Alexei
9
1999
Zeros and orthogonality of the Askey-Wilson polynomials for \(q\) a root of unity. Zbl 0882.33007
Spiridonov, Vyacheslav; Zhedanov, Alexei
9
1997
An analytic spin chain model with fractional revival. Zbl 1351.82044
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
9
2016
CMV matrices and little and big \(-1\) Jacobi polynomials. Zbl 1259.42018
Derevyagin, Maxim; Vinet, Luc; Zhedanov, Alexei
9
2012
The Hahn superalgebra and supersymmetric Dunkl oscillator models. Zbl 1280.81060
Genest, Vincent X.; Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
9
2013
Spectral transformations and generalized Pollaczek polynomials. Zbl 0956.33006
Yermolayeva, Oksana; Zhedanov, Alexei
8
1999
Representations of the Schrödinger group and matrix orthogonal polynomials. Zbl 1227.81173
Vinet, Luc; Zhedanov, Alexei
8
2011
A \(q\)-generalization of the para-Racah polynomials. Zbl 1390.33035
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
8
2018
“Leonard pairs” in classical mechanics. Zbl 1039.37047
Zhedanov, Alexei; Korovnichenko, Alyona
8
2002
New construction of \(3nj\)-symbols. Zbl 0856.22031
Granovskij, Ya. I.; Zhedanov, A. S.
8
1993
Tridiagonal representations of the \(q\)-oscillator algebra and Askey-Wilson polynomials. Zbl 1368.81074
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
8
2017
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
8
2016
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
8
2018
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
8
2013
Quasi-linear algebras and integrability (the Heisenberg picture). Zbl 1136.17019
Vinet, Luc; Zhedanov, Alexei
7
2008
Szegő polynomials on the real axis. Zbl 0939.33010
Vinet, Luc; Zhedanov, Alexei
7
1999
The \(q\)-Onsager algebra and multivariable \(q\)-special functions. Zbl 1375.81138
Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei
7
2017
The Heun-Racah and Heun-Bannai-Ito algebras. Zbl 1472.33011
Bergeron, Geoffroy; Crampé, Nicolas; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
7
2020
Truncation of the reflection algebra and the Hahn algebra. Zbl 1509.17009
Crampé, Nicolas; Ragoucy, Eric; Vinet, Luc; Zhedanov, Alexei
7
2019
Degenerate Sklyanin algebras, Askey-Wilson polynomials and Heun operators. Zbl 1519.81279
Gaboriaud, Julien; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
7
2020
Little and big \(q\)-Jacobi polynomials and the Askey-Wilson algebra. Zbl 1436.81070
Baseilhac, Pascal; Martin, Xavier; Vinet, Luc; Zhedanov, Alexei
7
2020
Generalized Bochner theorem: Characterization of the Askey-Wilson polynomials. Zbl 1140.33006
Vinet, Luc; Zhedanov, Alexei
6
2008
An algebraic model for the multiple Meixner polynomials of the first kind. Zbl 1251.81053
Miki, Hiroshi; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
6
2012
\(9j\)-symbols of the oscillator algebra and Krawtchouk polynomials in two variables. Zbl 0952.33010
Zhedanov, Alexei
6
1997
Two-dimensional Krall-Sheffer polynomials and integrable systems. Zbl 0995.33009
Harnad, John; Vinet, Luc; Yermolayeva, Oksana; Zhedanov, Alexei
6
2001
Hypergeometric orthogonal polynomials with respect to Newtonian bases. Zbl 1341.42045
Vinet, Luc; Zhedanov, Alexei
6
2016
On Dirichlet, Poncelet and Abel problems. Zbl 1264.14043
Burskii, Vladimir P.; Zhedanov, Alexei S.
6
2013
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
6
2018
Sklyanin-like algebras for \((q\)-)linear grids and \((q\)-)para-Krawtchouk polynomials. Zbl 1456.81265
Bergeron, Geoffroy; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei
6
2021
Elliptic grids, rational functions, and the Padé interpolation. Zbl 1136.42021
Spiridonov, V. P.; Zhedanov, A. S.
5
2007
Bispectrality and Darboux transformations in the theory of orthogonal polynomials. Zbl 0901.42015
Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei
5
1998
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
5
2001
Self-similarity, spectral transformations and orthogonal and biorthogonal polynomials. Zbl 1010.42014
Spiridonov, Vyacheslav; Zhedanov, Alexei
5
1999
Discrete reflectionless potentials, quantum algebras, and \(q\)-orthogonal polynomials. Zbl 0813.35098
Spiridonov, Vyacheslav; Zhedanov, Alexei
5
1995
Nonlinear shift \(q\)-Bose operators and \(q\)-coherent states. Zbl 0757.33007
Zhedanov, A. S.
5
1991
‘Twisted’ Clebsch-Gordan coefficients for \(SU_ q(2)\). Zbl 0765.17015
Granovskij, Ya. I.; Zhedanov, A. S.
5
1992
\(q\) rotations and other \(q\) transformations as unitary nonlinear automorphisms of quantum algebras. Zbl 0789.17011
Zhedanov, A. S.
5
1993
Bannai-Ito polynomials and dressing chains. Zbl 1304.42063
Derevyagin, Maxim; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
5
2014
The rational Heun operator and Wilson biorthogonal functions. Zbl 07690247
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
1
2023
Free boson realization of the Dunkl intertwining operator in one dimension. Zbl 1513.81074
Vinet, Luc; Zhedanov, Alexei
3
2022
Bispectrality and biorthogonality of the rational functions of \(q\)-Hahn type. Zbl 1519.33012
Bussière, Ismaël; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei
1
2022
A classical model for perfect transfer and fractional revival based on \(q\)-Racah polynomials. Zbl 1486.81118
Schérer, Hugo; Vinet, Luc; Zhedanov, Alexei
1
2022
Analytic “Newton’s cradles” with perfect transfer and fractional revival. Zbl 1487.81049
Schérer, Hugo; Vinet, Luc; Zhedanov, Alexei
1
2022
The rational Sklyanin algebra and the Wilson and para-Racah polynomials. Zbl 1508.17016
Bergeron, Geoffroy; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei
1
2022
Sklyanin-like algebras for \((q\)-)linear grids and \((q\)-)para-Krawtchouk polynomials. Zbl 1456.81265
Bergeron, Geoffroy; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei
6
2021
An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type. Zbl 1456.33011
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
5
2021
A unified algebraic underpinning for the Hahn polynomials and rational functions. Zbl 1459.33010
Vinet, Luc; Zhedanov, Alexei
5
2021
An algebraic treatment of the Askey biorthogonal polynomials on the unit circle. Zbl 1528.33016
Vinet, Luc; Zhedanov, Alexei
3
2021
The q-Heun operator of big q-Jacobi type and the q-Heun algebra. Zbl 1444.39007
Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei
14
2020
Heun algebras of Lie type. Zbl 1452.17024
Crampé, Nicolas; Vinet, Luc; Zhedanov, Alexei
11
2020
The Heun-Racah and Heun-Bannai-Ito algebras. Zbl 1472.33011
Bergeron, Geoffroy; Crampé, Nicolas; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
7
2020
Degenerate Sklyanin algebras, Askey-Wilson polynomials and Heun operators. Zbl 1519.81279
Gaboriaud, Julien; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
7
2020
Little and big \(q\)-Jacobi polynomials and the Askey-Wilson algebra. Zbl 1436.81070
Baseilhac, Pascal; Martin, Xavier; Vinet, Luc; Zhedanov, Alexei
7
2020
Signal processing, orthogonal polynomials, and Heun equations. Zbl 1443.33033
Bergeron, Geoffroy; Vinet, Luc; Zhedanov, Alexei
4
2020
Isospectral flows related to Frobenius-Stickelberger-Thiele polynomials. Zbl 1445.37052
Chang, Xiang-Ke; Hu, Xing-Biao; Szmigielski, Jacek; Zhedanov, Alexei
4
2020
Dunkl-supersymmetric orthogonal functions associated with classical orthogonal polynomials. Zbl 1514.42032
Luo, Yu; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
1
2020
The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type. Zbl 1423.33027
Baseilhac, Pascal; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
18
2019
The Heun operator of Hahn-type. Zbl 1429.33018
Vinet, Luc; Zhedanov, Alexei
17
2019
Truncation of the reflection algebra and the Hahn algebra. Zbl 1509.17009
Crampé, Nicolas; Ragoucy, Eric; Vinet, Luc; Zhedanov, Alexei
7
2019
The Higgs and Hahn algebras from a Howe duality perspective. Zbl 1476.81035
Frappat, Luc; Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei
5
2019
Double affine Hecke algebra of rank 1 and orthogonal polynomials on the unit circle. Zbl 1458.33008
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
4
2019
Perfect state transfer in a spin chain without mirror symmetry. Zbl 1509.82022
Coutinho, Gabriel; Vinet, Luc; Zhan, Hanmeng; Zhedanov, Alexei
2
2019
Algebraic Heun operator and band-time limiting. Zbl 1405.33025
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
34
2018
The Racah algebra as a commutant and Howe duality. Zbl 1411.81112
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei
15
2018
A \(q\)-generalization of the para-Racah polynomials. Zbl 1390.33035
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
8
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
8
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
6
2018
Supersymmetry of the quantum rotor. Zbl 1411.33016
Genest, Vincent X.; Vinet, Luc; Yu, Guo-Fu; Zhedanov, Alexei
2
2018
Symmetric abstract hypergeometric polynomials. Zbl 1375.33022
Tsujimoto, Satoshi; Vinet, Luc; Yu, Guo-Fu; Zhedanov, Alexei
1
2018
Tridiagonalization and the Heun equation. Zbl 1364.34126
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
25
2017
Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials. Zbl 1375.65059
Genest, Vincent X.; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
10
2017
Tridiagonal representations of the \(q\)-oscillator algebra and Askey-Wilson polynomials. Zbl 1368.81074
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
8
2017
The \(q\)-Onsager algebra and multivariable \(q\)-special functions. Zbl 1375.81138
Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei
7
2017
Exact state revival in a spin chain with next-to-nearest neighbour interactions. Zbl 1390.82011
Christandl, Matthias; Vinet, Luc; Zhedanov, Alexei
2
2017
Quantum spin chains with fractional revival. Zbl 1380.82030
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
21
2016
Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra. Zbl 1351.33010
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
21
2016
The non-symmetric Wilson polynomials are the Bannai-Ito polynomials. Zbl 1354.33010
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
18
2016
The para-Racah polynomials. Zbl 1333.33025
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
10
2016
An analytic spin chain model with fractional revival. Zbl 1351.82044
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
9
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
8
2016
Hypergeometric orthogonal polynomials with respect to Newtonian bases. Zbl 1341.42045
Vinet, Luc; Zhedanov, Alexei
6
2016
\(q\)-rotations and Krawtchouk polynomials. Zbl 1339.33020
Genest, Vincent X.; Post, Sarah; Vinet, Luc; Yu, Guo-Fu; Zhedanov, Alexei
5
2016
A Laplace-Dunkl equation on \(S^2\) and the Bannai-Ito algebra. Zbl 1311.22030
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
24
2015
Embeddings of the Racah algebra into the Bannai-Itô algebra. Zbl 1318.33027
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
17
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
5
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
55
2014
The Bannai-Ito polynomials as Racah coefficients of the \(sl_{-1}(2)\) algebra. Zbl 1304.17019
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
31
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
29
2014
The equitable Racah algebra from three \(\mathfrak {su}(1,1)\) algebras. Zbl 1355.17004
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
28
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
23
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
5
2014
Interbasis expansions for the isotropic 3D harmonic oscillator and bivariate Krawtchouk polynomials. Zbl 1283.81064
Genest, Vincent X.; 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
Elliptic solutions of the Toda chain and a generalization of the Stieltjes-Carlitz polynomials. Zbl 1298.33020
Zhedanov, Alexei
2
2014
Umbral “classical” polynomials. Zbl 1305.33024
Zhedanov, Alexei
1
2014
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
28
2013
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
18
2013
Bispectrality of the complementary Bannai-Itō polynomials. Zbl 1272.33010
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
15
2013
Dual \(-1\) Hahn polynomials: “classical” polynomials beyond the Leonard duality. Zbl 1300.33018
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
13
2013
The singular and the 2:1 anisotropic Dunkl oscillators in the plane. Zbl 1273.81089
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
11
2013
The Hahn superalgebra and supersymmetric Dunkl oscillator models. Zbl 1280.81060
Genest, Vincent X.; Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
9
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
8
2013
On Dirichlet, Poncelet and Abel problems. Zbl 1264.14043
Burskii, Vladimir P.; Zhedanov, Alexei S.
6
2013
Birth and death processes and quantum spin chains. Zbl 1285.82028
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
4
2013
A superintegrable finite oscillator in two dimensions with \(SU(2)\) symmetry. Zbl 1266.39011
Miki, Hiroshi; Post, Sarah; Vinet, Luc; Zhedanov, Alexei
4
2013
Dunkl shift operators and Bannai-Ito polynomials. Zbl 1248.33022
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
58
2012
Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer. Zbl 1251.81021
Vinet, Luc; Zhedanov, Alexei
28
2012
A limit \(q=-1\) for the big \(q\)-Jacobi polynomials. Zbl 1276.33019
Vinet, Luc; Zhedanov, Alexei
25
2012
\(d\)-orthogonal polynomials and \(\mathfrak {su}(2)\). Zbl 1238.33004
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
9
2012
CMV matrices and little and big \(-1\) Jacobi polynomials. Zbl 1259.42018
Derevyagin, Maxim; Vinet, Luc; Zhedanov, Alexei
9
2012
An algebraic model for the multiple Meixner polynomials of the first kind. Zbl 1251.81053
Miki, Hiroshi; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
6
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
36
2011
From \(\text{sl}_q(2)\) to a parabosonic Hopf algebra. Zbl 1246.17022
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
15
2011
Supersymmetric quantum mechanics with reflections. Zbl 1230.81032
Post, Sarah; Vinet, Luc; Zhedanov, Alexei
13
2011
A Bochner theorem for Dunkl polynomials. Zbl 1217.33022
Vinet, Luc; Zhedanov, Alexei
10
2011
Representations of the Schrödinger group and matrix orthogonal polynomials. Zbl 1227.81173
Vinet, Luc; Zhedanov, Alexei
8
2011
Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials. Zbl 1255.81143
Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei
5
2011
Jordan algebras and orthogonal polynomials. Zbl 1272.17031
Tsujimoto, Satoshi; 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
2
2011
Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum transformations. Zbl 1200.33013
Sasaki, Ryu; Tsujimoto, Satoshi; Zhedanov, Alexei
62
2010
The linear pencil approach to rational interpolation. Zbl 1193.41001
Beckermann, Bernhard; Derevyagin, Maxim; Zhedanov, Alexei
9
2010
Elliptic hypergeometric Laurent biorthogonal polynomials with a dense point spectrum on the unit circle. Zbl 1163.33325
Tsujimoto, Satoshi; Zhedanov, Alexei
16
2009
Automorphisms of the Heisenberg-Weyl algebra and \(d\)-orthogonal polynomials. Zbl 1202.33018
Vinet, Luc; Zhedanov, Alexei
16
2009
An operator approach to multipoint Padé approximations. Zbl 1163.41002
Derevyagin, Maxim S.; Zhedanov, Alexei S.
12
2009
Elliptic polynomials orthogonal on the unit circle with a dense point spectrum. Zbl 1178.33022
Zhedanov, Alexei
4
2009
Elliptic solutions of the restricted Toda chain, Lamé polynomials and generalization of the elliptic Stieltjes polynomials. Zbl 1179.33035
Vinet, Luc; Zhedanov, Alexei
2
2009
Quasi-linear algebras and integrability (the Heisenberg picture). Zbl 1136.17019
Vinet, Luc; Zhedanov, Alexei
7
2008
Generalized Bochner theorem: Characterization of the Askey-Wilson polynomials. Zbl 1140.33006
Vinet, Luc; Zhedanov, Alexei
6
2008
Toda chain, Stieltjes function, and orthogonal polynomials. Zbl 1121.37054
Peherstorfer, F.; Spiridonov, V. P.; Zhedanov, A. S.
18
2007
Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials. Zbl 1136.37041
Spiridonov, V. P.; Tsujimoto, S.; Zhedanov, A. S.
14
2007
Elliptic grids, rational functions, and the Padé interpolation. Zbl 1136.42021
Spiridonov, V. P.; Zhedanov, A. S.
5
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
Explicit multipoint rational interpolation Padé table for exponential and power functions. Zbl 1122.41008
Zhedanov, A.
2
2005
...and 54 more Documents
all top 5

Cited by 661 Authors

125 Vinet, Luc
90 Zhedanov, Alexei S.
44 Marcellán Español, Francisco
33 Crampé, Nicolas
28 Sri Ranga, Alagacone
28 Terwilliger, Paul M.
27 Durán, Antonio José
26 Tsujimoto, Satoshi
24 Genest, Vincent X.
18 Derevyagin, Maxim S.
18 Gaboriaud, Julien
17 Spiridonov, Vyacheslav Pavlovich
15 Huang, Hau-wen
14 Marquette, Ian
13 Baseilhac, Pascal
13 Chung, Won-Sang
13 De Bie, Hendrik
11 Alhaidari, Abdulaziz D.
11 Bracciali, Cleonice Fátima
11 Iliev, Plamen
11 Jordaan, Kerstin
11 Nomura, Kazumasa
10 Bernard, Pierre-Antoine
10 Chang, Xiangke
10 García-Ardila, Juan Carlos
10 Hassanabadi, Hassan
10 Odake, Satoru
9 Castillo, Kenier
9 Garza, Luis E.
9 Hu, Xingbiao
9 Pérez, Teresa E.
9 Poulain D’Andecy, Loïc
8 Bouzeffour, Fethi
8 Coutinho, Gabriel
8 Grünbaum, Francisco Alberto
8 Iwasaki, Masashi
8 Miki, Hiroshi
8 Quesne, Christiane
8 Zaimi, Meri
7 Bergeron, Geoffroy
7 Domínguez de la Iglesia, Manuel
7 Godsil, Christopher David
7 Ismail, Mourad El-Houssieny
7 Ito, Tatsuro
7 Mañas, Manuel
7 Swaminathan, Anbhu
7 van de Vijver, Wouter
7 Van der Jeugt, Joris
7 Zagorodnyuk, Sergey Mihaylovich
7 Zhan, Hanmeng
6 Area, Iván
6 Chan, Ada
6 Dominici, Diego Ernesto
6 Driver, Kathy A.
6 Frappat, Luc
6 Gómez-Ullate, David
6 Grandati, Yves
6 Lemay, Jean-Michel
6 Milson, Robert
6 Nakamura, Yoshimasa
6 Piñar, Miguel A.
6 Ragoucy, Eric
6 Rebocho, M. N.
6 Tamon, Christino
6 Van Assche, Walter
5 Bockting-Conrad, Sarah
5 Branquinho, Amílcar José Pinto Lopes
5 Chen, Xiaomin
5 Godoy, Eduardo Paciência
5 Huertas Cejudo, Edmundo José
5 Marriaga, Misael E.
5 Rains, Eric M.
5 Roy, Barnana
5 Sasaki, Ryu
5 Veronese, Daniel O.
5 Zhang, Yaozhong
4 Alfaro García, Manuel
4 Álvarez-Nodarse, Renato
4 Behera, Kiran Kumar
4 Cantero, María José
4 Choque Rivero, Abdon Eddy
4 De Clercq, Hadewijch
4 Filipuk, Galina V.
4 Ghazouani, Sami
4 He, Yi
4 Hernández, Javier
4 Khorozov, Emil Ivanov
4 Koelink, Erik
4 Koornwinder, Tom H.
4 Kwon, Kil Hyun
4 Lamblém, Regina Litz
4 Latini, Danilo
4 Li, Shihao
4 Moral, Leandro
4 Nepomechie, Rafael I.
4 Peña, Ana
4 Rezola, María Luisa
4 Rosengren, Hjalmar
4 Sedaghatnia, Parisa
4 van Diejen, Jan Felipe
...and 561 more Authors
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Cited in 158 Serials

78 Journal of Mathematical Physics
49 Journal of Approximation Theory
49 Journal of Physics A: Mathematical and Theoretical
41 Linear Algebra and its Applications
39 Journal of Mathematical Analysis and Applications
32 Journal of Computational and Applied Mathematics
23 Proceedings of the American Mathematical Society
22 Integral Transforms and Special Functions
22 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
20 Letters in Mathematical Physics
19 Nuclear Physics. B
16 The Ramanujan Journal
15 Communications in Mathematical Physics
13 Journal of Difference Equations and Applications
12 Numerical Algorithms
11 Physics Letters. A
11 Applied Mathematics and Computation
10 Advances in Mathematics
10 Annals of Physics
9 Constructive Approximation
8 Theoretical and Mathematical Physics
8 Physica D
8 Annales Henri Poincaré
7 Modern Physics Letters A
7 Journal of Algebra
7 Journal of High Energy Physics
5 Communications in Algebra
5 International Journal of Theoretical Physics
5 Rocky Mountain Journal of Mathematics
5 Mathematics of Computation
5 Acta Applicandae Mathematicae
5 Indagationes Mathematicae. New Series
5 Computational and Applied Mathematics
4 International Journal of Modern Physics A
4 Reviews in Mathematical Physics
4 Journal of Combinatorial Theory. Series A
4 Studies in Applied Mathematics
4 Transactions of the American Mathematical Society
4 Applied Numerical Mathematics
4 Journal of Mathematical Sciences (New York)
4 St. Petersburg Mathematical Journal
4 The Electronic Journal of Combinatorics
4 Journal of Algebra and its Applications
4 Mediterranean Journal of Mathematics
4 Analysis and Mathematical Physics
4 Bulletin of Mathematical Sciences
3 Journal d’Analyse Mathématique
3 Physica A
3 Reports on Mathematical Physics
3 Ukrainian Mathematical Journal
3 Duke Mathematical Journal
3 Journal of Nonlinear Mathematical Physics
3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
3 Computational Methods and Function Theory
3 Quantum Information Processing
3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
3 Journal of Classical Analysis
2 Applicable Analysis
2 Computers & Mathematics with Applications
2 Discrete Mathematics
2 Journal of Statistical Physics
2 Linear and Multilinear Algebra
2 Nonlinearity
2 Periodica Mathematica Hungarica
2 Calcolo
2 Journal of Differential Equations
2 Journal of Functional Analysis
2 Journal of Pure and Applied Algebra
2 Journal of Statistical Planning and Inference
2 Advances in Applied Mathematics
2 SIAM Journal on Discrete Mathematics
2 Russian Mathematics
2 Journal of Algebraic Combinatorics
2 Filomat
2 Selecta Mathematica. New Series
2 ELA. The Electronic Journal of Linear Algebra
2 Journal of Inequalities and Applications
2 Regular and Chaotic Dynamics
2 Journal of Modern Optics
2 Journal of Systems Science and Complexity
2 International Journal of Geometric Methods in Modern Physics
2 Journal of Statistical Mechanics: Theory and Experiment
2 Boundary Value Problems
2 Forum of Mathematics, Sigma
1 International Journal of Modern Physics B
1 Computer Physics Communications
1 Discrete Applied Mathematics
1 Journal of Engineering Mathematics
1 Journal of Geometry and Physics
1 Annales de l’Institut Fourier
1 Canadian Mathematical Bulletin
1 Colloquium Mathematicum
1 Journal of Applied Probability
1 Journal of the London Mathematical Society. Second Series
1 Journal of Number Theory
1 Le Matematiche
1 Mathematische Nachrichten
1 Nagoya Mathematical Journal
1 Numerische Mathematik
1 Results in Mathematics
...and 58 more Serials
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Cited in 52 Fields

474 Special functions (33-XX)
253 Quantum theory (81-XX)
245 Harmonic analysis on Euclidean spaces (42-XX)
116 Nonassociative rings and algebras (17-XX)
86 Dynamical systems and ergodic theory (37-XX)
80 Linear and multilinear algebra; matrix theory (15-XX)
67 Combinatorics (05-XX)
58 Difference and functional equations (39-XX)
55 Operator theory (47-XX)
54 Ordinary differential equations (34-XX)
48 Partial differential equations (35-XX)
40 Associative rings and algebras (16-XX)
37 Statistical mechanics, structure of matter (82-XX)
32 Functions of a complex variable (30-XX)
31 Numerical analysis (65-XX)
26 Topological groups, Lie groups (22-XX)
24 Approximations and expansions (41-XX)
21 Mechanics of particles and systems (70-XX)
20 Group theory and generalizations (20-XX)
19 Probability theory and stochastic processes (60-XX)
18 Algebraic geometry (14-XX)
17 Number theory (11-XX)
13 Real functions (26-XX)
7 Global analysis, analysis on manifolds (58-XX)
7 Relativity and gravitational theory (83-XX)
6 Functional analysis (46-XX)
5 Differential geometry (53-XX)
5 Optics, electromagnetic theory (78-XX)
4 Measure and integration (28-XX)
4 Geometry (51-XX)
4 Statistics (62-XX)
3 Field theory and polynomials (12-XX)
3 Commutative algebra (13-XX)
3 Sequences, series, summability (40-XX)
3 Integral transforms, operational calculus (44-XX)
3 Manifolds and cell complexes (57-XX)
3 Information and communication theory, circuits (94-XX)
2 General algebraic systems (08-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Abstract harmonic analysis (43-XX)
2 Integral equations (45-XX)
2 Convex and discrete geometry (52-XX)
2 Computer science (68-XX)
2 Biology and other natural sciences (92-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Potential theory (31-XX)
1 General topology (54-XX)
1 Algebraic topology (55-XX)
1 Mechanics of deformable solids (74-XX)
1 Fluid mechanics (76-XX)
1 Astronomy and astrophysics (85-XX)
1 Systems theory; control (93-XX)

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