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## Koornwinder, Tom H.

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 Author ID: koornwinder.tom-h Published as: Koornwinder, Tom H.; Koornwinder, T. H.; Koornwinder, Tom External Links: MGP · Wikidata · GND · IdRef
 Documents Indexed: 115 Publications since 1971, including 8 Books 8 Contributions as Editor 1 Further Contribution
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#### Co-Authors

 74 single-authored 4 Askey, Richard Allen 3 Diekema, Enno 3 Flensted-Jensen, Mogens 3 Koelink, Erik 3 Stokman, Jasper V. 2 Bais, F. Alexander 2 Dijkhuizen, Mathijs S. 2 Ismail, Mourad El-Houssieny 2 Muller, N. M. 2 Schlosser, Michael J. 2 Sprinkhuizen-Kuyper, Ida G. 2 Swarttouw, René F. 2 Van Assche, Walter 1 Atakishiev, Natig M. 1 Atakishiyeva, Mesuma K. 1 Badertscher, Erich 1 Bouzeffour, Fethi 1 Braaksma, Boele L. J. 1 Brummelhuis, Raymond 1 Butzer, Paul Leo 1 Cagliero, Leandro 1 Carnovale, Giovanna 1 Ciccoli, Nicola 1 Dijksma, Aad 1 Dorlas, Tony C. 1 Faraut, Jacques 1 Gasper, George Jun 1 Koekoek, Roelof 1 Koepf, Wolfram A. 1 Kostenko, Aleksey S. 1 Kuznetsov, Vadim Borisovich 1 Lesky, Peter A. 1 Lodder, Jan J. 1 Mazzocco, Marta 1 Nevai, Paul G. 1 Onn, Uri 1 Rahman, Mizan 1 Rösler, Margit 1 Sauter, Stefan A. 1 Schempp, Walter Johannes 1 Schroers, Bernd J. 1 Schwartz, Alan L. 1 Sharapudinov, Idris Idrisovich 1 Slingerland, Johannes K. 1 Stanton, Dennis W. 1 Stegeman, Jan D. 1 Teschl, Gerald 1 van der Meer, H. A. 1 van Dijk, Gerrit 1 van Hemmen, J. Leo 1 Voit, Michael 1 Walter, Gilbert G. 1 Warnaar, S. Ole
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#### Serials

 9 SIAM Journal on Mathematical Analysis 5 Journal of Approximation Theory 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae 3 Journal of Mathematical Analysis and Applications 3 Arkiv för Matematik 3 Indagationes Mathematicae 3 Journal of Computational and Applied Mathematics 3 Indagationes Mathematicae. New Series 2 Canadian Journal of Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Complex Variables. Theory and Application 2 Methods and Applications of Analysis 2 The Ramanujan Journal 1 Applicable Analysis 1 Communications in Mathematical Physics 1 Journal of Mathematical Physics 1 Letters in Mathematical Physics 1 Mathematics of Computation 1 Advances in Mathematics 1 Canadian Mathematical Bulletin 1 Compositio Mathematica 1 Geometriae Dedicata 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Combinatorial Theory. Series A 1 Proceedings of the American Mathematical Society 1 Studies in Applied Mathematics 1 Transactions of the American Mathematical Society 1 Journal of Symbolic Computation 1 Constructive Approximation 1 CWI Quarterly 1 L’Enseignement Mathématique. 2e Série 1 Journal of Physics A: Mathematical and General 1 Nieuw Archief voor Wiskunde. Derde Serie 1 SIAM Journal on Applied Mathematics 1 St. Petersburg Mathematical Journal 1 Kyushu Journal of Mathematics 1 Journal of Lie Theory 1 Séminaire Lotharingien de Combinatoire 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 Analysis and Applications (Singapore) 1 Mathematics and its Applications (Dordrecht) 1 Journal of Physics A: Mathematical and Theoretical 1 Springer Monographs in Mathematics
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#### Fields

 92 Special functions (33-XX) 23 Abstract harmonic analysis (43-XX) 22 Topological groups, Lie groups (22-XX) 18 Harmonic analysis on Euclidean spaces (42-XX) 16 Nonassociative rings and algebras (17-XX) 6 General and overarching topics; collections (00-XX) 6 Group theory and generalizations (20-XX) 6 Functional analysis (46-XX) 6 Numerical analysis (65-XX) 5 History and biography (01-XX) 5 Combinatorics (05-XX) 5 Associative rings and algebras (16-XX) 5 Integral transforms, operational calculus (44-XX) 5 Quantum theory (81-XX) 3 Functions of a complex variable (30-XX) 3 Differential geometry (53-XX) 3 Computer science (68-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Real functions (26-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Number theory (11-XX) 1 Partial differential equations (35-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

105 Publications have been cited 2,068 times in 1,268 Documents Cited by Year
Hypergeometric orthogonal polynomials and their $$q$$-analogues. With a foreword by Tom H. Koornwinder. Zbl 1200.33012
Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F.
2010
A new proof of a Paley-Wiener type theorem for the Jacobi transform. Zbl 0303.42022
Koornwinder, Tom
1975
Orthogonal polynomials with weight function $$(1- x)^{\alpha}(1+x)^{\beta}+M\delta(x+1)+N\delta(x-1)$$. Zbl 0507.33005
Koornwinder, Tom H.
1984
On $$q$$-analogues of the Fourier and Hankel transforms. Zbl 0759.33007
Koornwinder, Tom H.; Swarttouw, René F.
1992
The convolution structure for Jacobi function expansions. Zbl 0267.42009
Flensted-Jensen, Mogens; Koornwinder, Tom
1973
Askey-Wilson polynomials for root systems of type $$BC$$. Zbl 0797.33014
Koornwinder, Tom H.
1992
Two-variable analogues of the classical orthogonal polynomials. Zbl 0326.33002
Koornwinder, Tom
1975
Askey-Wilson polynomials as zonal spherical functions on the $$SU(2)$$ quantum group. Zbl 0799.33015
Koornwinder, Tom H.
1993
Compact quantum groups and $$q$$-special functions. Zbl 0821.17015
Koornwinder, Tom H.
1994
Representations of the twisted SU(2) quantum group and some q- hypergeometric orthogonal polynomials. Zbl 0681.22020
Koornwinder, T. H.
1989
Jacobi functions and analysis on noncompact semisimple Lie groups. Zbl 0584.43010
Koornwinder, Tom H.
1984
CQG algebras: A direct algebraic approach to compact quantum groups. Zbl 0861.17005
Dijkhuizen, Mathijs S.; Koornwinder, Tom H.
1994
Special functions and $$q$$-commuting variables. Zbl 0882.33014
Koornwinder, Tom H.
1997
Quantum homogeneous spaces, duality and quantum 2-spheres. Zbl 0818.17017
Dijkhuizen, Mathijs S.; Koornwinder, Tom H.
1994
The addition formula for Jacobi polynomials and spherical harmonics. Zbl 0276.33023
Koornwinder, Tom
1973
Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators. III, IV. Zbl 0291.33013
Koornwinder, Tom H.
1974
Jacobi functions: the addition formula and the positivity of the dual convolution structure. Zbl 0409.33009
Flensted-Jensen, Mogens; Koornwinder, Tom H.
1979
Jacobi polynomials. II: An analytic proof of the product formula. Zbl 0242.33020
Koornwinder, Tom
1974
Positivity proofs for linearization and connection coefficients of orthogonal polynomials satisfying an addition formula. Zbl 0386.33009
Koornwinder, Tom
1978
On Zeilberger’s algorithm and its $$q$$-analogue. Zbl 0797.65011
Koornwinder, Tom H.
1993
The relationship between Zhedanov’s algebra $$AW(3)$$ and the double affine Hecke algebra in the rank one case. Zbl 1134.33321
Koornwinder, Tom H.
2007
Zhedanov’s algebra $$AW(3)$$ and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra. Zbl 1157.33328
Koornwinder, Tom H.
2008
$$q$$-special functions, a tutorial. Zbl 0768.33018
Koelink, H. T.; Koornwinder, T. H.
1992
The addition formula for little $$q$$-Legendre polynomials and the $$SU(2)$$ quantum group. Zbl 0738.33012
Koornwinder, Tom H.
1991
The addition formula for Jacobi polynomials. I: Summary of results. Zbl 0247.33017
Koornwinder, T. H.
1972
The addition formula for Jacobi polynomials. II: The Laplace type integral representation and the product formula. Zbl 0247.33018
Koornwinder, T. H.
1972
Krawtchouk polynomials, a unification of two different group theoretic interpretations. Zbl 0505.33015
Koornwinder, Tom H.
1982
Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle. Zbl 0937.33009
Koornwinder, T. H.; Schwartz, A. L.
1997
Meixner-Pollaczek polynomials and the Heisenberg algebra. Zbl 0672.33011
Koornwinder, Tom H.
1989
Jacobi functions as limit cases of q-ultraspherical polynomials. Zbl 0713.33010
Koornwinder, Tom H.
1990
Wavelets: an elementary treatment of theory and applications. Zbl 0832.00013
1993
A note on the absolute bound for systems of lines. Zbl 0328.05020
Koornwinder, Tom H.
1976
Limit transitions for BC type multivariable orthogonal polynomials. Zbl 0881.33026
Stokman, Jasper V.; Koornwinder, Tom H.
1997
Special orthogonal polynomial systems mapped onto each other by the Fourier-Jacobi transform. Zbl 0592.42005
Koornwinder, T. H.
1985
The addition formula for Jacobi polynomials. III: Completion of the proof. Zbl 0247.33019
Koornwinder, T. H.
1972
Orthogonal polynomials in connection with quantum groups. Zbl 0697.42019
Koornwinder, Tom H.
1990
The structure relation for Askey-Wilson polynomials. Zbl 1120.33018
Koornwinder, Tom H.
2007
Tensor product representations of the quantum double of a compact group. Zbl 0944.20033
Koornwinder, T. H.; Bais, F. A.; Muller, N. M.
1998
Jacobi polynomials. III: An analytic proof of the addition formula. Zbl 0299.33012
Koornwinder, Tom
1975
Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators. I, II. Zbl 0263.33011
Koornwinder, Tom H.
1974
Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials. Zbl 1318.33013
Cagliero, Leandro; Koornwinder, Tom H.
2015
On the equivalence of two fundamental theta identities. Zbl 1379.11049
Koornwinder, Tom H.
2014
The addition formula for Laguerre polynomials. Zbl 0361.33002
Koornwinder, Tom
1977
The quantum double of a (locally) compact group. Zbl 0892.16023
Koornwinder, T. H.; Muller, N. M.
1997
Weighted permutation problems and Laguerre polynomials. Zbl 0405.05008
1978
On an identity by Chaundy and Bullard. I. Zbl 1210.05014
Koornwinder, Tom H.; Schlosser, Michael J.
2008
Differentiation by integration using orthogonal polynomials, a survey. Zbl 1259.65050
Diekema, Enno; Koornwinder, Tom H.
2012
Generalized power series expansions for a class of orthogonal polynomials in two variables. Zbl 0395.33008
Koornwinder, Tom; Sprinkhuizen-Kuyper, Ida
1978
Special functions: Group theoretical aspects and applications. Zbl 0543.00007
1984
$$q$$-special functions and their occurence in quantum groups. Zbl 0770.33012
Koornwinder, T. H.
1992
$$q$$-Laguerre polynomials and big $$q$$-Bessel functions and their orthogonality relations. Zbl 0964.33008
Ciccoli, Nicola; Koelink, Erik; Koornwinder, Tom H.
1999
The Clebsch-Gordan coefficients for the quantum group $$S_{\mu}U(2)$$ and q-Hahn polynomials. Zbl 0708.22007
Koelink, H. T.; Koornwinder, T. H.
1989
Fourier transform and the Verlinde formula for the quantum double of a finite group. Zbl 0958.20038
Koornwinder, T. H.; Schroers, B. J.; Slingerland, J. K.; Bais, F. A.
1999
The Askey scheme as a four-manifold with corners. Zbl 1195.33053
Koornwinder, Tom H.
2009
Spherical harmonics and the product of two Jacobi polynomials. Zbl 0209.09302
Dijksma, A.; Koornwinder, T. H.
1971
The finite continuous Jacobi transform and its inverse. Zbl 0683.44002
Koornwinder, Tom H.; Walter, Gilbert G.
1990
Dualities in the $$q$$-Askey scheme and degenerate DAHA. Zbl 1408.33032
Koornwinder, Tom H.; Mazzocco, Marta
2018
On an identity by Chaundy and Bullard. II: More history. Zbl 1282.33008
Koornwinder, Tom H.; Schlosser, Michael J.
2013
Positive definite spherical functions on a non-compact, rank one symmetric space. Zbl 0433.43014
Flensted-Jensen, Mogens; Koornwinder, Tom H.
1979
Clebsch-Gordan coefficients for SU(2) and Hahn polynomials. Zbl 0483.20027
Koornwinder, T. H.
1981
A note on the multiplicity free reduction of certain orthogonal and unitary groups. Zbl 0498.22014
Koornwinder, Tom H.
1982
An intergral of products of ultraspherical functions and a q-extension. Zbl 0564.33008
Askey, Richard; Koornwinder, Tom H.; Rahman, Mizan
1986
Matrix elements of irreducible representations of SU(2)$$\times SU(2)$$ and vector-valued orthogonal polynomials. Zbl 0581.22020
Koornwinder, Tom H.
1985
Group theoretic interpretations of Askey’s scheme of hypergeometric orthogonal polynomials. Zbl 0654.33006
Koornwinder, Tom H.
1988
LU factorizations, $$q = 0$$ limits, and $$p$$-adic interpretations of some $$q$$-hypergeometric orthogonal polynomials. Zbl 1120.33019
Koornwinder, Tom H.; Onn, Uri
2007
Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators. Zbl 1325.33003
Koornwinder, Tom H.
2015
Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials. Zbl 1216.33040
Koornwinder, Tom H.; Bouzeffour, Fethi
2011
Identities of nonterminating series by Zeilberger’s algorithm. Zbl 0945.65015
Koornwinder, Tom H.
1998
Limit transition between hypergeometric functions of type BC and type A. Zbl 1405.33019
Rösler, Margit; Koornwinder, Tom; Voit, Michael
2013
Asymptotic behaviour for Wall polynomials and the addition formula for little $$q$$-Legendre polynomials. Zbl 0738.33003
Van Assche, Walter; Koornwinder, Tom H.
1991
Yet another proof of the addition formula for Jacobi polynomials. Zbl 0406.33006
Koornwinder, Tom
1977
The addition formula for Jacobi polynomials and the theory of orthogonal polynomials in two variables, a survey. Zbl 0297.33021
Koornwinder, T. H.
1974
Lowering and raising operators for some special orthogonal polynomials. Zbl 1132.33315
Koornwinder, Tom H.
2006
On some limit cases of Askey-Wilson polynomials. Zbl 0913.33008
Stokman, J. V.; Koornwinder, T. H.
1998
Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator. Zbl 1405.33012
Koornwinder, Tom; Kostenko, Aleksey; Teschl, Gerald
2018
Integral representations for Horn’s $$H_2$$ function and Olsson’s $$F_P$$ function. Zbl 1447.33009
Diekema, Enno; Koornwinder, Tom H.
2019
A $$q$$-analogue of convolution on the line. Zbl 1004.33013
Carnovale, G.; Koornwinder, T. H.
2000
Discrete hypergroups associated with compact quantum Gelfand pairs. Zbl 0824.17018
Koornwinder, Tom H.
1995
On the limit from $$q$$-Racah polynomials to big $$q$$-Jacobi polynomials. Zbl 1218.33018
Koornwinder, Tom H.
2011
Continuous Hahn polynomials of differential operator argument and analysis on Riemannian symmetric spaces of constant curvature. Zbl 0759.33006
1992
Lie groups and Lie algebras. Zbl 0428.22005
Koornwinder, T. H.
1979
Research announcement. Continuous q-Legendre polynomials are spherical matrix elements of irreducible representations of the quantum SU(2) group. Zbl 0677.33008
Koornwinder, Tom H.
1989
Okounkov’s BC-type interpolation Macdonald polynomials and their $$q=1$$ limit. Zbl 1331.33038
Koornwinder, Tom H.
2015
Special functions associated with root systems: a first introduction for non-specialists. Zbl 0924.33008
Koornwinder, Tom H.
1998
Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation. Zbl 0960.17004
Koornwinder, Tom H.
2000
Positive convolution structures associated with quantum groups. Zbl 0823.60007
Koornwinder, Tom H.
1991
Handling hypergeometric series in Maple. Zbl 0833.33001
Koornwinder, Tom H.
1991
Jacobi polynomials of type $$BC$$, Jack polynomials, limit transitions and $$O(\infty)$$. Zbl 0968.33500
Koornwinder, Tom H.
1995
Special functions associated with root systems: Recent progress. Zbl 0863.33015
Koornwinder, Tom H.
1995
Dual addition formulas associated with dual product formulas. Zbl 1411.33010
Koornwinder, Tom H.
2018
Invariant differential operators on non-reductive homogeneous spaces. Zbl 0454.22006
Koornwinder, T. H.
1981
The representation theory of SL(2,R), a non-infinitesimal approach. Zbl 0495.22010
Koornwinder, Tom H.
1982
Gauss hypergeometric function and quadratic $$R$$-matrix algebras. Zbl 0841.33002
Koornwinder, T. H.; Kuznetsov, V. B.
1994
The mathematical contributions of Richard Askey. Zbl 0953.01015
Gasper, George; Ismail, Mourad E. H.; Koornwinder, Tom; Nevai, Paul; Stanton, Dennis
2000
Quadratic transformations for orthogonal polynomials in one and two variables. Zbl 1409.33007
Koornwinder, Tom H.
2018
A second addition formula for continuous $$q$$-ultraspherical polynomials. Zbl 1219.33025
Koornwinder, Tom H.
2005
Generalizations of an integral for Legendre polynomials by Persson and Strang. Zbl 1237.33005
Diekema, Enno; Koornwinder, Tom H.
2012
$$q$$-extension of Mehta’s eigenvectors of the finite Fourier transform for $$q$$, a root of unity. Zbl 1183.33035
Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.
2009
A group theoretic interpretation of the last part of de Branges’ proof of the Bieberbach conjecture. Zbl 0608.30021
Koornwinder, Tom H.
1986
Hypergeometric functions of $$2\times 2$$ matrix argument are expressible in terms of Appell’s functions $$F_4$$. Zbl 0394.33004
Koornwinder, Tom; Sprinkhuizen-Kuyper, Ida
1978
Integral representations for Horn’s $$H_2$$ function and Olsson’s $$F_P$$ function. Zbl 1447.33009
Diekema, Enno; Koornwinder, Tom H.
2019
Dualities in the $$q$$-Askey scheme and degenerate DAHA. Zbl 1408.33032
Koornwinder, Tom H.; Mazzocco, Marta
2018
Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator. Zbl 1405.33012
Koornwinder, Tom; Kostenko, Aleksey; Teschl, Gerald
2018
Dual addition formulas associated with dual product formulas. Zbl 1411.33010
Koornwinder, Tom H.
2018
Quadratic transformations for orthogonal polynomials in one and two variables. Zbl 1409.33007
Koornwinder, Tom H.
2018
Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials. Zbl 1318.33013
Cagliero, Leandro; Koornwinder, Tom H.
2015
Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators. Zbl 1325.33003
Koornwinder, Tom H.
2015
Okounkov’s BC-type interpolation Macdonald polynomials and their $$q=1$$ limit. Zbl 1331.33038
Koornwinder, Tom H.
2015
A tribute to Dick Askey. Zbl 1315.01039
2015
The intersection of bivariate orthogonal polynomials on triangle patches. Zbl 1309.65145
Koornwinder, Tom H.; Sauter, Stefan A.
2015
On the equivalence of two fundamental theta identities. Zbl 1379.11049
Koornwinder, Tom H.
2014
On an identity by Chaundy and Bullard. II: More history. Zbl 1282.33008
Koornwinder, Tom H.; Schlosser, Michael J.
2013
Limit transition between hypergeometric functions of type BC and type A. Zbl 1405.33019
Rösler, Margit; Koornwinder, Tom; Voit, Michael
2013
Differentiation by integration using orthogonal polynomials, a survey. Zbl 1259.65050
Diekema, Enno; Koornwinder, Tom H.
2012
Generalizations of an integral for Legendre polynomials by Persson and Strang. Zbl 1237.33005
Diekema, Enno; Koornwinder, Tom H.
2012
Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials. Zbl 1216.33040
Koornwinder, Tom H.; Bouzeffour, Fethi
2011
On the limit from $$q$$-Racah polynomials to big $$q$$-Jacobi polynomials. Zbl 1218.33018
Koornwinder, Tom H.
2011
Hypergeometric orthogonal polynomials and their $$q$$-analogues. With a foreword by Tom H. Koornwinder. Zbl 1200.33012
Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F.
2010
The Askey scheme as a four-manifold with corners. Zbl 1195.33053
Koornwinder, Tom H.
2009
$$q$$-extension of Mehta’s eigenvectors of the finite Fourier transform for $$q$$, a root of unity. Zbl 1183.33035
Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.
2009
Zhedanov’s algebra $$AW(3)$$ and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra. Zbl 1157.33328
Koornwinder, Tom H.
2008
On an identity by Chaundy and Bullard. I. Zbl 1210.05014
Koornwinder, Tom H.; Schlosser, Michael J.
2008
The relationship between Zhedanov’s algebra $$AW(3)$$ and the double affine Hecke algebra in the rank one case. Zbl 1134.33321
Koornwinder, Tom H.
2007
The structure relation for Askey-Wilson polynomials. Zbl 1120.33018
Koornwinder, Tom H.
2007
LU factorizations, $$q = 0$$ limits, and $$p$$-adic interpretations of some $$q$$-hypergeometric orthogonal polynomials. Zbl 1120.33019
Koornwinder, Tom H.; Onn, Uri
2007
Lowering and raising operators for some special orthogonal polynomials. Zbl 1132.33315
Koornwinder, Tom H.
2006
A second addition formula for continuous $$q$$-ultraspherical polynomials. Zbl 1219.33025
Koornwinder, Tom H.
2005
A $$q$$-analogue of convolution on the line. Zbl 1004.33013
Carnovale, G.; Koornwinder, T. H.
2000
Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation. Zbl 0960.17004
Koornwinder, Tom H.
2000
The mathematical contributions of Richard Askey. Zbl 0953.01015
Gasper, George; Ismail, Mourad E. H.; Koornwinder, Tom; Nevai, Paul; Stanton, Dennis
2000
$$q$$-Laguerre polynomials and big $$q$$-Bessel functions and their orthogonality relations. Zbl 0964.33008
Ciccoli, Nicola; Koelink, Erik; Koornwinder, Tom H.
1999
Fourier transform and the Verlinde formula for the quantum double of a finite group. Zbl 0958.20038
Koornwinder, T. H.; Schroers, B. J.; Slingerland, J. K.; Bais, F. A.
1999
Tensor product representations of the quantum double of a compact group. Zbl 0944.20033
Koornwinder, T. H.; Bais, F. A.; Muller, N. M.
1998
Identities of nonterminating series by Zeilberger’s algorithm. Zbl 0945.65015
Koornwinder, Tom H.
1998
On some limit cases of Askey-Wilson polynomials. Zbl 0913.33008
Stokman, J. V.; Koornwinder, T. H.
1998
Special functions associated with root systems: a first introduction for non-specialists. Zbl 0924.33008
Koornwinder, Tom H.
1998
Special functions and $$q$$-commuting variables. Zbl 0882.33014
Koornwinder, Tom H.
1997
Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle. Zbl 0937.33009
Koornwinder, T. H.; Schwartz, A. L.
1997
Limit transitions for BC type multivariable orthogonal polynomials. Zbl 0881.33026
Stokman, Jasper V.; Koornwinder, Tom H.
1997
The quantum double of a (locally) compact group. Zbl 0892.16023
Koornwinder, T. H.; Muller, N. M.
1997
Discrete hypergroups associated with compact quantum Gelfand pairs. Zbl 0824.17018
Koornwinder, Tom H.
1995
Jacobi polynomials of type $$BC$$, Jack polynomials, limit transitions and $$O(\infty)$$. Zbl 0968.33500
Koornwinder, Tom H.
1995
Special functions associated with root systems: Recent progress. Zbl 0863.33015
Koornwinder, Tom H.
1995
Compact quantum groups and $$q$$-special functions. Zbl 0821.17015
Koornwinder, Tom H.
1994
CQG algebras: A direct algebraic approach to compact quantum groups. Zbl 0861.17005
Dijkhuizen, Mathijs S.; Koornwinder, Tom H.
1994
Quantum homogeneous spaces, duality and quantum 2-spheres. Zbl 0818.17017
Dijkhuizen, Mathijs S.; Koornwinder, Tom H.
1994
Gauss hypergeometric function and quadratic $$R$$-matrix algebras. Zbl 0841.33002
Koornwinder, T. H.; Kuznetsov, V. B.
1994
Askey-Wilson polynomials as zonal spherical functions on the $$SU(2)$$ quantum group. Zbl 0799.33015
Koornwinder, Tom H.
1993
On Zeilberger’s algorithm and its $$q$$-analogue. Zbl 0797.65011
Koornwinder, Tom H.
1993
Wavelets: an elementary treatment of theory and applications. Zbl 0832.00013
1993
On $$q$$-analogues of the Fourier and Hankel transforms. Zbl 0759.33007
Koornwinder, Tom H.; Swarttouw, René F.
1992
Askey-Wilson polynomials for root systems of type $$BC$$. Zbl 0797.33014
Koornwinder, Tom H.
1992
$$q$$-special functions, a tutorial. Zbl 0768.33018
Koelink, H. T.; Koornwinder, T. H.
1992
$$q$$-special functions and their occurence in quantum groups. Zbl 0770.33012
Koornwinder, T. H.
1992
Continuous Hahn polynomials of differential operator argument and analysis on Riemannian symmetric spaces of constant curvature. Zbl 0759.33006
1992
The addition formula for little $$q$$-Legendre polynomials and the $$SU(2)$$ quantum group. Zbl 0738.33012
Koornwinder, Tom H.
1991
Asymptotic behaviour for Wall polynomials and the addition formula for little $$q$$-Legendre polynomials. Zbl 0738.33003
Van Assche, Walter; Koornwinder, Tom H.
1991
Positive convolution structures associated with quantum groups. Zbl 0823.60007
Koornwinder, Tom H.
1991
Handling hypergeometric series in Maple. Zbl 0833.33001
Koornwinder, Tom H.
1991
Jacobi functions as limit cases of q-ultraspherical polynomials. Zbl 0713.33010
Koornwinder, Tom H.
1990
Orthogonal polynomials in connection with quantum groups. Zbl 0697.42019
Koornwinder, Tom H.
1990
The finite continuous Jacobi transform and its inverse. Zbl 0683.44002
Koornwinder, Tom H.; Walter, Gilbert G.
1990
Representations of the twisted SU(2) quantum group and some q- hypergeometric orthogonal polynomials. Zbl 0681.22020
Koornwinder, T. H.
1989
Meixner-Pollaczek polynomials and the Heisenberg algebra. Zbl 0672.33011
Koornwinder, Tom H.
1989
The Clebsch-Gordan coefficients for the quantum group $$S_{\mu}U(2)$$ and q-Hahn polynomials. Zbl 0708.22007
Koelink, H. T.; Koornwinder, T. H.
1989
Research announcement. Continuous q-Legendre polynomials are spherical matrix elements of irreducible representations of the quantum SU(2) group. Zbl 0677.33008
Koornwinder, Tom H.
1989
Group theoretic interpretations of Askey’s scheme of hypergeometric orthogonal polynomials. Zbl 0654.33006
Koornwinder, Tom H.
1988
An intergral of products of ultraspherical functions and a q-extension. Zbl 0564.33008
Askey, Richard; Koornwinder, Tom H.; Rahman, Mizan
1986
A group theoretic interpretation of the last part of de Branges’ proof of the Bieberbach conjecture. Zbl 0608.30021
Koornwinder, Tom H.
1986
Special orthogonal polynomial systems mapped onto each other by the Fourier-Jacobi transform. Zbl 0592.42005
Koornwinder, T. H.
1985
Matrix elements of irreducible representations of SU(2)$$\times SU(2)$$ and vector-valued orthogonal polynomials. Zbl 0581.22020
Koornwinder, Tom H.
1985
Orthogonal polynomials with weight function $$(1- x)^{\alpha}(1+x)^{\beta}+M\delta(x+1)+N\delta(x-1)$$. Zbl 0507.33005
Koornwinder, Tom H.
1984
Jacobi functions and analysis on noncompact semisimple Lie groups. Zbl 0584.43010
Koornwinder, Tom H.
1984
Special functions: Group theoretical aspects and applications. Zbl 0543.00007
1984
Krawtchouk polynomials, a unification of two different group theoretic interpretations. Zbl 0505.33015
Koornwinder, Tom H.
1982
A note on the multiplicity free reduction of certain orthogonal and unitary groups. Zbl 0498.22014
Koornwinder, Tom H.
1982
The representation theory of SL(2,R), a non-infinitesimal approach. Zbl 0495.22010
Koornwinder, Tom H.
1982
Clebsch-Gordan coefficients for SU(2) and Hahn polynomials. Zbl 0483.20027
Koornwinder, T. H.
1981
Invariant differential operators on non-reductive homogeneous spaces. Zbl 0454.22006
Koornwinder, T. H.
1981
Jacobi functions: the addition formula and the positivity of the dual convolution structure. Zbl 0409.33009
Flensted-Jensen, Mogens; Koornwinder, Tom H.
1979
Positive definite spherical functions on a non-compact, rank one symmetric space. Zbl 0433.43014
Flensted-Jensen, Mogens; Koornwinder, Tom H.
1979
Lie groups and Lie algebras. Zbl 0428.22005
Koornwinder, T. H.
1979
Representations of locally compact groups with applications. Part I, II. Zbl 0418.00005
1979
Positivity proofs for linearization and connection coefficients of orthogonal polynomials satisfying an addition formula. Zbl 0386.33009
Koornwinder, Tom
1978
Weighted permutation problems and Laguerre polynomials. Zbl 0405.05008
1978
Generalized power series expansions for a class of orthogonal polynomials in two variables. Zbl 0395.33008
Koornwinder, Tom; Sprinkhuizen-Kuyper, Ida
1978
Hypergeometric functions of $$2\times 2$$ matrix argument are expressible in terms of Appell’s functions $$F_4$$. Zbl 0394.33004
Koornwinder, Tom; Sprinkhuizen-Kuyper, Ida
1978
The addition formula for Laguerre polynomials. Zbl 0361.33002
Koornwinder, Tom
1977
Yet another proof of the addition formula for Jacobi polynomials. Zbl 0406.33006
Koornwinder, Tom
1977
Harmonics and spherical functions on Grassmann manifolds of rank two and two-variable analogues of Jacobi polynomials. Zbl 0343.33009
Koornwinder, Tom
1977
A note on the absolute bound for systems of lines. Zbl 0328.05020
Koornwinder, Tom H.
1976
A new proof of a Paley-Wiener type theorem for the Jacobi transform. Zbl 0303.42022
Koornwinder, Tom
1975
Two-variable analogues of the classical orthogonal polynomials. Zbl 0326.33002
Koornwinder, Tom
1975
Jacobi polynomials. III: An analytic proof of the addition formula. Zbl 0299.33012
Koornwinder, Tom
1975
Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators. III, IV. Zbl 0291.33013
Koornwinder, Tom H.
1974
Jacobi polynomials. II: An analytic proof of the product formula. Zbl 0242.33020
Koornwinder, Tom
1974
Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators. I, II. Zbl 0263.33011
Koornwinder, Tom H.
1974
The addition formula for Jacobi polynomials and the theory of orthogonal polynomials in two variables, a survey. Zbl 0297.33021
Koornwinder, T. H.
1974
The convolution structure for Jacobi function expansions. Zbl 0267.42009
Flensted-Jensen, Mogens; Koornwinder, Tom
1973
The addition formula for Jacobi polynomials and spherical harmonics. Zbl 0276.33023
Koornwinder, Tom
1973
...and 5 more Documents
all top 5

#### Cited by 1,198 Authors

 30 Koelink, Erik 23 Vinet, Luc 22 Koornwinder, Tom H. 19 Marcellán Español, Francisco 18 Álvarez-Nodarse, Renato 18 Fitouhi, Ahmed 17 Xu, Yuan 16 Bouzeffour, Fethi 16 Ismail, Mourad El-Houssieny 16 Markett, Clemens 15 Area, Iván 14 Trimèche, Khalifa 14 Zhedanov, Alexei S. 13 Mimachi, Katsuhisa 13 Terwilliger, Paul M. 12 Godoy, Eduardo Paciência 11 Carroll, Robert W. 11 Daher, Radouan 11 Dhaouadi, Lazhar 11 Koepf, Wolfram A. 11 van Diejen, Jan Felipe 10 Bavinck, Herman 10 Gorbachëv, Dmitriĭ Viktorovich 10 Groenevelt, Wolter G. M. 10 Kwon, Kil Hyun 10 Littlejohn, Lance L. 10 Stokman, Jasper V. 9 Chirvăsitu, Alexandru 9 Kawazoe, Takeshi 9 Menegatto, Valdir Antonio 9 Ronveaux, André 8 Everitt, William Norrie 8 Genest, Vincent X. 8 Van Assche, Walter 7 Bettaibi, Néji 7 Flensted-Jensen, Mogens 7 Gupta, Vijay 7 Iliev, Plamen 7 Koekoek, Roelof 7 Peron, Ana Paula 7 Piñar, Miguel A. 7 Rahman, Mizan 7 Román, Pablo Manuel 7 Voit, Michael 7 Zarzo, Alejandro 6 Annaby, Mahmoud H. 6 Brahim, Kamel 6 De Commer, Kenny 6 Grünbaum, Francisco Alberto 6 Huang, Hau-wen 6 Li, Huiyuan 6 Masjed-Jamei, Mohammad 6 Neretin, Yuriĭ Aleksandrovich 6 Noumi, Masatoshi 6 Pérez, Teresa E. 6 Rains, Eric M. 6 Warnaar, S. Ole 6 Zayed, Ahmed I. 5 Abreu, Luís Daniel 5 Awonusika, Richard Olu 5 Binous, Wafa 5 dos Santos Cardoso, José Luís 5 Chen, William Yong-Chuan 5 Crampé, Nicolas 5 Delcamp, Clement 5 Dijkhuizen, Mathijs S. 5 El Ouadih, Salah 5 Emsiz, Erdal 5 Jordaan, Kerstin 5 Kalnins, Ernest G. 5 Lewanowicz, Stanisław 5 Meaney, Christopher 5 Nemri, Akram 5 Nomura, Kazumasa 5 Ol’shanskiĭ, Grigoriĭ Iosifovich 5 Rösler, Margit 4 Anker, Jean-Philippe 4 Bais, F. Alexander 4 Bannai, Eiichi 4 Baseilhac, Pascal 4 Betancor-Ortiz, Juan Diego 4 Betancor Perez, Jorge Juan 4 Camporesi, Roberto 4 Damaskinskij, E. V. 4 de Laat, Tim 4 Diekema, Enno 4 Elmonser, Hédi Ben 4 Fernández, Lidia 4 Floreanini, Roberto 4 Gallardo, Léonard 4 Ito, Tatsuro 4 Kanjin, Yuichi 4 Kim, Taekyun 4 Kushpel, Alexander K. 4 Lasser, Rupert 4 Méndez, J. M. R. 4 Mhaskar, Hrushikesh N. 4 Miller, Willard jun. 4 Nevo, Amos 4 Rafaeli, Fernando Rodrigo ...and 1,098 more Authors
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#### Cited in 269 Serials

 70 Journal of Computational and Applied Mathematics 65 Journal of Mathematical Analysis and Applications 50 Journal of Approximation Theory 41 Journal of Mathematical Physics 41 Integral Transforms and Special Functions 40 Proceedings of the American Mathematical Society 35 The Ramanujan Journal 28 Advances in Mathematics 26 Communications in Mathematical Physics 26 Journal of Functional Analysis 25 Indagationes Mathematicae. New Series 24 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 23 Transactions of the American Mathematical Society 20 Constructive Approximation 16 Letters in Mathematical Physics 16 Journal of Symbolic Computation 16 Journal of High Energy Physics 15 Journal of Algebra 14 Applied Mathematics and Computation 14 Linear Algebra and its Applications 14 Journal of Difference Equations and Applications 12 Applicable Analysis 12 Rocky Mountain Journal of Mathematics 12 Journal of Geometry and Physics 12 Publications of the Research Institute for Mathematical Sciences, Kyoto University 11 Nuclear Physics. B 11 Duke Mathematical Journal 10 Compositio Mathematica 10 The Journal of Fourier Analysis and Applications 9 Computers & Mathematics with Applications 8 Communications in Algebra 8 Arkiv för Matematik 8 Journal of Combinatorial Theory. Series A 8 Advances in Applied Mathematics 8 Numerical Algorithms 8 Advances in Difference Equations 7 Journal of Computational Physics 7 Mathematical Notes 7 Mathematische Annalen 7 Acta Applicandae Mathematicae 7 Journal of Pseudo-Differential Operators and Applications 6 Discrete Mathematics 6 Journal d’Analyse Mathématique 6 Theoretical and Mathematical Physics 6 European Journal of Combinatorics 6 Positivity 6 Journal of the Australian Mathematical Society 5 Ukrainian Mathematical Journal 5 Mathematics of Computation 5 Acta Mathematica 5 Functional Analysis and its Applications 5 Journal of Pure and Applied Algebra 5 Mathematische Zeitschrift 5 Proceedings of the Japan Academy. Series A 5 Tohoku Mathematical Journal. Second Series 5 Journal of Theoretical Probability 5 Applied Mathematics Letters 5 Journal of Mathematical Sciences (New York) 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 International Journal of Mathematics and Mathematical Sciences 4 Numerische Mathematik 4 Results in Mathematics 4 Studies in Applied Mathematics 4 International Journal of Mathematics 4 Annales Mathématiques Blaise Pascal 4 Selecta Mathematica. New Series 4 Journal of Nonlinear Mathematical Physics 4 Journal of Algebra and its Applications 4 Analysis and Applications (Singapore) 4 Chebyshevskiĭ Sbornik 4 Complex Analysis and Operator Theory 4 Analysis and Mathematical Physics 4 Korean Journal of Mathematics 3 Analysis Mathematica 3 Bulletin of the Australian Mathematical Society 3 Israel Journal of Mathematics 3 Inventiones Mathematicae 3 Journal of Number Theory 3 Mathematische Nachrichten 3 Monatshefte für Mathematik 3 Tokyo Journal of Mathematics 3 Applied Numerical Mathematics 3 Journal of Scientific Computing 3 The Journal of Geometric Analysis 3 Designs, Codes and Cryptography 3 Bulletin of the American Mathematical Society. New Series 3 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 3 Expositiones Mathematicae 3 The Journal of Analysis 3 Kyushu Journal of Mathematics 3 Bulletin des Sciences Mathématiques 3 Abstract and Applied Analysis 3 Algebras and Representation Theory 3 Infinite Dimensional Analysis, Quantum Probability and Related Topics 3 Annales Henri Poincaré 3 Czechoslovak Journal of Physics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Mediterranean Journal of Mathematics 3 Advances in Pure and Applied Mathematics 3 Journal of Spectral Theory ...and 169 more Serials
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#### Cited in 55 Fields

 674 Special functions (33-XX) 257 Harmonic analysis on Euclidean spaces (42-XX) 166 Abstract harmonic analysis (43-XX) 150 Quantum theory (81-XX) 142 Nonassociative rings and algebras (17-XX) 104 Combinatorics (05-XX) 89 Topological groups, Lie groups (22-XX) 89 Integral transforms, operational calculus (44-XX) 89 Functional analysis (46-XX) 79 Approximations and expansions (41-XX) 78 Ordinary differential equations (34-XX) 76 Associative rings and algebras (16-XX) 68 Operator theory (47-XX) 67 Numerical analysis (65-XX) 66 Partial differential equations (35-XX) 64 Difference and functional equations (39-XX) 55 Group theory and generalizations (20-XX) 44 Probability theory and stochastic processes (60-XX) 42 Global analysis, analysis on manifolds (58-XX) 38 Functions of a complex variable (30-XX) 36 Number theory (11-XX) 30 Linear and multilinear algebra; matrix theory (15-XX) 29 Differential geometry (53-XX) 24 Real functions (26-XX) 18 Relativity and gravitational theory (83-XX) 18 Information and communication theory, circuits (94-XX) 17 Statistical mechanics, structure of matter (82-XX) 16 Dynamical systems and ergodic theory (37-XX) 15 Computer science (68-XX) 14 Manifolds and cell complexes (57-XX) 11 Geometry (51-XX) 10 Potential theory (31-XX) 10 Convex and discrete geometry (52-XX) 9 Algebraic geometry (14-XX) 9 Several complex variables and analytic spaces (32-XX) 8 Fluid mechanics (76-XX) 6 Category theory; homological algebra (18-XX) 6 Sequences, series, summability (40-XX) 6 Integral equations (45-XX) 6 Mechanics of deformable solids (74-XX) 5 Statistics (62-XX) 4 History and biography (01-XX) 4 Commutative algebra (13-XX) 4 Measure and integration (28-XX) 4 Geophysics (86-XX) 4 Operations research, mathematical programming (90-XX) 3 Mathematical logic and foundations (03-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Mechanics of particles and systems (70-XX) 3 Systems theory; control (93-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Optics, electromagnetic theory (78-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Field theory and polynomials (12-XX) 1 Biology and other natural sciences (92-XX)

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