Tom Koornwinder's research and overview papers

See also:

• my papers reviewed at MathSciNet (you need a subscription),
• the list of my arXiv preprints on http://arxiv.org/a/koornwinder_t_1,
• my author's profile at Zentralblatt Math.
• my page at Orcid

If you don't have access to any of my papers listed below which you would like to see, please contact me, and I will send it to you.

2024   2023   2022   2021   2019   2018   2017   2015   2014   2013   2012   2011   2010   2009   2008   2007   2006   2005   2003   2000   1999   1998   1997   1995   1994   1993   1992   1991   1990   1989   1988   1986   1985   1984   1983   1982   1981   1980   1979   1978   1977   1976   1975   1974   1973   1972   1971

2024

• T.H. Koornwinder and M. Mazzocco, Automorphisms of the DAHA of type C₁ˇC₁ and their action on Askey-Wilson polynomials and functions. I. The flip (a,b,c,d) ↦ (a,b,qd⁻¹,qc⁻¹), arXiv:2407.17366v1 [math.CA], 24 July 2024.

• T.H. Koornwinder, Charting the q-Askey scheme. III. Verde-Star scheme for q=1, arXiv:2307.06668v2 [math.CA], 2024; to appear in: Orthogonal polynomials and special functions, K. Castillo and A. J. Duràn (eds.), Springer-Verlag, 2024.

2023

• T.H. Koornwinder, Dual addition formulas: the case of continuous q-ultraspherical and q-Hermite polynomials, Ramanujan J. 61 (2023), 425-444; arXiv:1803.09636v3 [math.CA].

• T.H. Koornwinder, Charting the q-Askey scheme. II. The q-Zhedanov scheme, Indag. Math. (N.S.) 34 (2023), 317-337; Errata: Indag. Math. (N.S.) 34 (2023), 1419-1420 (for mixed up citation numbers in the journal article); or more convenient, consult the arXiv version arXiv:2209.07995v3 [math.CA].

• N. Hoshi, M. Katori, T.H. Koornwinder and M.J. Schlosser, On an identity of Chaundy and Bullard. III. Basic and elliptic extensions, arXiv:2304.10003v2 [math.CO], 2023;  to appear in Contemp. Math. AMS.

• T.H. Koornwinder, q-Special functions, an overview, arXiv:math/0511148v2 [math.CA],
  5 Aug 2023; to appear in Encyclopedia of Mathematical Physics, 2nd edition, Elsevier. (This updates the article in the first edition, 2006.)

2022

• T.H. Koornwinder, Charting the q-Askey scheme, in Hypergeometry, Integrability and Lie Theory, Contemporary Mathematics 780 (2022), 79-94;  MR4476417;  arXiv:2108.03858v2 [math.CA]. See errata (last modified July 24, 2023).

2021

• N. Disveld, T.H. Koornwinder and J.V. Stokman, A nonsymmetric version of Okounkov's BC-type interpolation Macdonald polynomials, Transformation Groups 26 (2021), 1261-1292;  MR4372946;  arXiv:1808.01221v5 [math.QA]; see errata and a comment.

• T. H. Koornwinder and J. V. Stokman, General overview of multivariable special functions, in: Encyclopedia of special functions: The Askey-Bateman project, Vol. II: Multivariable special functions, Cambridge University Press, 2021, pp. 1-18;  MR4421385,
  See preliminary version.

2019

• P.L. Butzer and T.H. Koornwinder, Josef Meixner: his life and his orthogonal polynomials, Indag. Math. (N.S.) 30 (2019), 250-264;  MR3906134;  Zbl 1405.33010;  arXiv:1609.02588v5 [math.HO];  errata (last modified 5 Janury 2024).

• E. Diekema and T.H. Koornwinder, Integral representations for Horn's H_2 function and Olsson's F_P function, Kyushu J. Math. 73 (2019), 1-24,  MR4028083;  Zbl 07131226;  arXiv:1607.07349v7 [math.CA].

2018

• T.H. Koornwinder, Dual addition formulas associated with dual product formulas,  in: Frontiers in Orthogonal Polynomials and q-Series, World Scientific, 2018,
  Ch. 19, pp. 373-392;  MR3791629;   arXiv:1607.06053v5 [math.CA]; errata.

• T. Koornwinder, A. Kostenko and G. Teschl, Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator, Adv. Math. 333 (2018), 796-821;  MR3818091;  slightly extended version in arXiv:1602.08626v3 [math.CA].

• T.H. Koornwinder, Quadratic transformations for orthogonal polynomials in one and two variables, in: Representation theory, Special Functions and Painlevé Equations, Adv. Stud. Pure Math., Vol. 76, Math. Soc. Japan, Tokyo, 2018, pp. 418-447;  arXiv:1512.09294v2 [math.CA].

• T.H. Koornwinder and M. Mazzocco, Dualities in the q-Askey scheme and degenerate DAHA, Studies Appl. Math. 141 (2018), 424-473;  arXiv:1803.02775v3 [math.CA];  errata.

2017

• V.A. Pessers and T.H. Koornwinder, Approximation systems, arXiv:1205.6370v3 [math.CA], 19 October 2017.

• T.H. Koornwinder, Dual addition formula for continuous q-ultraspherical polynomials, in: Proceedings of the 16th Annual Conference SSFA, Vol. 16, , 2017, pp. 1–29, SSFA;   arXiv:2102.12131v1 [math.CA] (first part);  arXiv:1803.09636v3 [math.CA] (second part).

2015

• L. Cagliero and T.H. Koornwinder, Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials, J. Approx. Theory 193 (2015), 20-38;  MR3324561;  arXiv:1301.4887v5 [math.CA];  see errata.

• T.H. Koornwinder and S.A. Sauter, The intersection of bivariate orthogonal polynomials on triangle patches, Math. Comp. 84 (2015), 1795-1812;  MR3335892;  arXiv:1307.8429v3 [math.NA].

• T.H. Koornwinder, Okounkov's BC-type interpolation Macdonald polynomials and their q=1 limit, Sém. Lothar. Combin. B72a (2015), 27 pp.;  MR3383151;  errata;  arXiv:1408.5993v5 [math.CA].

• T.H. Koornwinder, Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators, SIGMA 11 (2015), 074, 22 pp.;  MR3400036;  arXiv:1504.08144v3 [math.CA].

• T.H. Koornwinder, Additions to the formula lists in "Hypergeometric orthogonal polynomials and their q-analogues" by Koekoek, Lesky and Swarttouw, arXiv:1401.0815v2 [math.CA], 12 January 2015. An update made 4 February 2022 is available here (not yet on arXiv).

2014

• T.H. Koornwinder, On the equivalence of two fundamental theta identities, Anal. Appl. (Singap.) 12 (2014), 711-725;  MR3271026;  arXiv:1401.5368v3 [math.CA].

• E.G.F. Thomas (with an Appendix by T.H. Koornwinder), A polarization identity for multilinear maps, Indag. Math. (N.S.) 25 (2014), 468-474;  arXiv:1309.1275v4 [math.FA].

2013

• T.H. Koornwinder and M.J. Schlosser, On an identity by Chaundy and Bullard. II. More history, Indag. Math. (N.S.) 24 (2013), 174-180;  arXiv:1205.6362v2 [math.CA];  errata to the journal version;  further material.

• M. Rösler, T. Koornwinder and M. Voit, Limit transition between hypergeometric functions of type BC and type A, Compositio Math. 149 (2013), 1381-1400;  arXiv:1207.0487v3 [math.CA].

• T.H. Koornwinder, Orthogonal polynomials, in: Computer algebra in quantum field theory
  (C. Schneider & J. Blümlein, eds.), Springer-Verlag, 2013, pp. 145-170; 
  slightly corrected arXiv version Orthogonal polynomials, a short survey, arXiv:1303.2825v2 [math.CA], November 2021.

2012

• E. Diekema and T.H. Koornwinder, Generalizations of an integral for Legendre polynomials by Persson and Strang, J. Math. Anal. Appl. 388 (2012), 125-135;  MR2869734;  arXiv:1005.2285v2 [math.CA].

• E. Diekema and T.H. Koornwinder, Differentiation by integration using orthogonal polynomials, a survey, J. Approx. Theory 164 (2012), 637-667;  MR2903122;  arXiv:1102.5219v3 [math.CA];   errata to the journal version.

• T.H. Koornwinder, Askey-Wilson polynomial, Scholarpedia 7 (2012), no.7, 7761.

2011

• T.H. Koornwinder and F. Bouzeffour, Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials, Appl. Anal. 90 (2011), 731-746;  Zbl 1216.33040;  arXiv:1006.1140v3 [math.CA];  see errata in journal version (already corrected in last arXiv version).

• T.H. Koornwinder, On the limit from q-Racah polynomials to big q-Jacobi polynomials, SIGMA 7 (2011), 040, 8 pp.; arXiv:1011.5585v4 [math.CA].

2010

• T.H. Koornwinder, R. Wong. R. Koekoek and R.F. Swarttouw, Orthogonal polynomials, Chapter 18 in NIST Handbook of Mathematical Functions, Cambridge University Press, 2010; also Chapter 18 in NIST Digital Library of Mathematical Functions;  MR2655358.

• T. Koornwinder, Foreword to the book Hypergeometric orthogonal polynomials and their q-analogues by R. Koekoek, P.A. Lesky and R.F. Swarttouw, Springer-Verlag, 2010; pp. v-x in Front Matter.

2009

• T.H. Koornwinder, The Askey scheme as a four-manifold with corners, Ramanujan J. 20 (2009), 409-439;  MR2574781;  arXiv:0909.2822v2 [math.CA];  erratum;  related notebooks.

• M.K. Atakishiyeva, N.M. Atakishiyev and T.H. Koornwinder, On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity, J. Phys. A 42 (2009) 454004 (9 pp.);  MR2556646;  arXiv:0811.4100v2 [math.CA].

2008

• T.H. Koornwinder and M.J. Schlosser, On an identity by Chaundy and Bullard. I, Indag. Math. (N.S.) 19 (2008), 239-261;  MR2489329;  arXiv:0712.2125v3 [math.CA].

• T.H. Koornwinder, Zhedanov's algebra AW(3) and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra, SIGMA 4 (2008), 052, 17 pages;   MR2425640;  arXiv:0711.2320v3 [math.QA];  errata.

2007

• T.H. Koornwinder and U. Onn, LU factorizations, q=0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials, Ramanujan J. 13 (2007), 365-387;  MR2281172;  arXiv:math/0405309v4 [math.CA].

• T.H. Koornwinder, The structure relation for Askey-Wilson polynomials, J. Comput. Appl. Math. 207 (2007), 214-226;  MR2345243;  arXiv:math/0601303v3 [math.CA];   see correction and comment (last modified 30 September 2021).

• T.H. Koornwinder, The relationship between Zhedanov's algebra AW(3) and the double affine Hecke algebra in the rank one case, SIGMA 3 (2007), 063, 15 pages;  MR2299864;  arXiv:math/0612730v4 [math.QA], 7 Nov 2007;  related notebooks (last modified 18 September 2015;  a comment;  see errata.

2006

• T.H. Koornwinder, q-Special functions, in: Encyclopedia of Mathematical Physics, J.-P. Françoise, G.L. Naber and S.T. Tsou (eds.), Elsevier, Oxford, 2006, ISBN 978-0-1251-2666-3, Vol. 4. pp. 105-116;  slightly extended preprint version in arXiv:math/0511148v1 [math.CA], 6 Nov 2005.

• T.H. Koornwinder, Lowering and raising operators for some special orthogonal polynomials, in Jack, Hall-Littlewood and Macdonald polynomials, V.B. Kuznetsov and S. Sahi (eds.), Contemporary Mathematics 417, American Mathematical Society, 2006, pp. 227-238;  MR2284130;  arXiv:math/0505378v1 [math.CA].

• T. Koornwinder, Proof of formula (4.15), Appendix E to the paper: S. de Haro and A.C. Petkou, Instantons and conformal holography, J. High Energy Phys. 12 (2006), paper 076;  MR2276678;  arXiv:hep-th/0606276v3.

2005

• T.H. Koornwinder, A second addition formula for continuous q-ultraspherical polynomials, in Theory and Applications of Special Functions. A Volume Dedicated to Mizan Rahman, M.E.H. Ismail and E. Koelink (eds.), Developments in Mathematics, Vol. 13, Springer-Verlag, 2005, pp. 339-360;  MR2132469;  arXiv:math/0303211v2 [math.CA].

2003

• T.H. Koornwinder and N. Touhami, Fusion and exchange matrices for quantized sl(2) and associated q-special functions, arXiv:math.QA/0207159 v2, 2003.

2000

• T.H. Koornwinder and N. Touhami, QDYBE: some explicit formulas for exchange matrix and related objects in case of sl(2), q=1, arXiv:math.QA/0007086, 2000.

• G. Carnovale and T.H. Koornwinder, A q-analogue of convolution on the line, Methods Appl. Anal. 7 (2000), 705-726;  MR1868553;  arXiv:math.CA/9909025 v3.

• T.H. Koornwinder, Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation, Int. J. Math. Math. Sci. 24 (2000), 793-806;  MR1794602;  arXiv:math.QA/0007079.

1999

• T.H. Koornwinder, B.J. Schroers, J.K. Slingerland and F.A. Bais, Fourier transform and the Verlinde formula for the quantum double of a finite group, J. Phys. A 32 (1999), 8539-8549; MR 2001d:20046; arXiv:math.QA/9904029 v2.

• N. Ciccoli, E. Koelink and T.H. Koornwinder, q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations, Methods Appl. Anal. 6 (1999), 109-127; MR 2002b:33017; arXiv:math.CA/9805023.

1998

• T.H. Koornwinder, Identities of nonterminating series by Zeilberger's algorithm, J. Comput. Appl. Math. 99 (1998), 449-461; MR 2000j:33004; arXiv:math.CA/9805010.

• T.H. Koornwinder, F.A. Bais and N.M. Muller, Tensor product representations of the quantum double of a compact group, Comm. Math. Phys. 198 (1998), 157-186; MR 2000b:81068; arXiv:q-alg 9712042.

• T.H. Koornwinder, Special functions associated with root systems: a first introduction for non-specialists, pp. 10-24 in Special functions and differential equations, K. Srinivasa Rao, R. Jagannathan, G. Vanden Berghe and J. Van der Jeugt (eds.), Allied Publishers, New Delhi, 1998; MR 99h:33056; pdf of preprint, updated 1999.

• J.V. Stokman and T.H. Koornwinder, On some limit cases of Askey-Wilson polynomials, J. Approx. Theory 95 (1998), 310-330; MR 99k:33052; pdf of preprint.

1997

• J.V. Stokman and T.H. Koornwinder, Limit transitions for BC type multivariable orthogonal polynomials, Canad. J. Math. 49 (1997), 373-404; MR 98g:33031; pdf of preprint.

• T.H. Koornwinder, Special functions and q-commuting variables, in Special Functions, q-Series and Related Topics, M.E.H. Ismail, D.R. Masson and M. Rahman (eds.), Fields Institute Communications 14, American Mathematical Society, 1997, pp. 131-166; MR 99e:33024; arXiv:q-alg/9608008.

• T.H. Koornwinder and A.L. Schwartz, Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle, Constr. Approx. 11 (1997), 537-567; MR 99b:33024; pdf of preprint.

• T.H. Koornwinder and N.M. Muller, The quantum double of a (locally) compact group, J. Lie Theory 7 (1997), 101-120; 8 (1998), 187; MR1450746; arXiv:q-alg/9605044; pdf of erratum.

1995

• T.H. Koornwinder, Discrete hypergroups associated with compact quantum Gelfand pairs, in Applications of hypergroups and related measure algebras, W.C. Connett, M.-O. Gebuhrer and A.L. Schwartz (eds.), Contemporary Mathematics 183, 1995, American Mathematical Society, pp. 213-235;  MR1334779;  arXiv:math/9403217v2 [math.QA].

• T.H. Koornwinder, Jacobi polynomials of type BC, Jack polynomials, limit transitions and O(infinity), in: Mathematical analysis, wavelets and signal processing, M.E.H. Ismail e.a. (eds.), Contemporary Mathematics 190, 1995, American Mathematical Society, pp. 283-286; MR1354860; arXiv:math.CA/9307216.

1994

• T.H. Koornwinder and V.B. Kuznetsov, Gauss hypergeometric function and quadratic R-matrix algebras, Algebra i Analiz 6 (1994), No.3, 161-184; St. Petersburg Math. J. 6 (1995), No.3, 595-618; MR 95i:33002; arXiv:math.QA/9403218.

• M.S. Dijkhuizen and T.H. Koornwinder, Quantum homogeneous spaces, duality, and quantum 2-spheres, Geom. Dedicata 52 (1994), 291-315; MR 95i:16037; pdf of preprint.

• M.S. Dijkhuizen and T.H. Koornwinder, CQG algebras: a direct algebraic approach to compact quantum groups, Lett. Math. Phys. 32 (1994), 315-330;  MR1310296;
  arXiv:hep-th/9406042.

• T.H. Koornwinder, Compact quantum groups and q-special functions, in: Representations of Lie groups and quantum groups, V. Baldoni and M.A. Picardello (eds.), Pitman Research Notes in Mathematics Series 311, Longman Scientific & Technical, 1994, pp. 46-128; MR1431306.
  • preprint of Chapters 1,2: General compact quantum groups, a tutorial, arXiv:hep-th/9401114v1.
  • preprint of Chapters 3,4: q-Special functions, a tutorial, arXiv:math/9403216v2 [math.CA] (last modified 14 Oct 2013).

• T.H. Koornwinder, Special functions associated with root systems: recent progress, in: From Universal Morphisms to Megabytes --- a Baayen Space Odyssey, K.R. Apt, A. Schrijver and N.M. Temme (eds.), CWI, Amsterdam, 1994, pp. 391-404; MR1490602; arXiv:math.CA/9411227.

1993

• T.H. Koornwinder, Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group, SIAM J. Math. Anal. 24 (1993), 795-813; MR 94k:33042; pdf of preprint (updated and corrected on August 5, 2005).

• T.H. Koornwinder, On Zeilberger's algorithm and its $q$-analogue, J. Comput. Appl. Math. 48 (1993), 91-111; MR 95b:33011;
  pdf of slightly extended preprint version On Zeilberger's algorithm and its q-analogue: a rigorous description, updated January 2001.

• Wavelets: an elementary treatment of theory and applications, T.H. Koornwinder (ed.), World Scientific, 1993, ISBN 981-02-1388-3 (hardcover), 981-02-2486-9 (pbk); MR 94c:42001.
  • P.W. Hemker, T.H. Koornwinder and N.M. Temme, Wavelets: mathematical preliminaries, pp. 13-26; MR 94h:42059; pdf of scan.
  • T.H. Koornwinder, The continuous wavelet transform, pp. 27-48; MR 94i:42044.
  • T.H. Koornwinder, Fast wavelet transform and Calderón-Zygmund operators, pp. 161-182; MR 94k:42051.

• T.H. Koornwinder, Uniform multi-parameter limit transitions in the Askey tableau, arXiv:math.CA/9309213, 1993.

1992

• T.H. Koornwinder, Askey-Wilson polynomials for root systems of type BC, in: Hypergeometric functions on domains of positivity, Jack polynomials, and applications, D.St.P. Richards (ed.), Contemp. Math. 138, Amer. Math. Soc., 1992, pp. 189-204; MR 94e:33039; pdf of preprint.

• T.H. Koornwinder and R.F. Swarttouw, On q-Analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc. 333 (1992), 445-461;  MR1069750;
  arXiv:1208.2521v1 [math.CA]  (13 August 2012; contains corrections of Proposition 4.2 and Proposition A.1).

• E. Badertscher and T.H. Koornwinder, Continuous Hahn polynomials of differential operator argument and analysis on Riemannian symmetric spaces of constant curvature, Canad. J. Math. 44 (1992), 750-773; MR 94k:43011; pdf of preprint.

1991

• T.H. Koornwinder, The addition formula for little q-Legendre polynomials and the SU(2) quantum group, SIAM J. Math. Anal. 22 (1991), 295-301; MR 92f:33025.

• W. Van Assche and T.H. Koornwinder, Asymptotic behaviour for Wall polynomials and the addition formula for little q-Legendre polynomials, SIAM J. Math. Anal. 22 (1991), 302-311; MR 92f:33026.

• T.H. Koornwinder, Handling hypergeometric series in Maple, in: Orthogonal polynomials and their applications, C. Brezinski, L. Gori and A. Ronveaux (eds.), IMACS Annals on Computing and Applied Mathematics 9, Baltzer, 1991, pp. 73-80; MR 95f:33006;  fulltext (pdf) with updated references.

• T.H. Koornwinder, Positive convolution structures associated with quantum groups, in: Probability Measures on Groups X, H. Heyer (ed.), Plenum, 1991, pp. 249-268; MR1178988; pdf of scan; errata.

1990

• T.H. Koornwinder, Jacobi functions as limit cases of q-ultraspherical polynomials, J. Math. Anal. Appl. 148 (1990), 44-54; MR 91c:33033.

• T.H. Koornwinder and G.G. Walter, The finite continuous Jacobi transform and its inverse, J. Approx. Theory 60 (1990), 83-100; MR 91g:44003.

• T.H. Koornwinder, Orthogonal polynomials in connection with quantum groups, in: Orthogonal polynomials: theory and practice, P. Nevai (ed.), NATO ASI Series C 294, Kluwer, 1990, pp. 257-292; MR 92i:33018; pdf of preprint.

1989

• T.H. Koornwinder, Representations of the twisted SU(2) quantum group and some q-hypergeometric orthogonal polynomials, Nederl. Akad. Wetensch. Proc. Ser. A 92 = Indag. Math. 51 (1989), 97-117; MR 90h:17016;  pdf of scan of the paper.

• H.T. Koelink and T.H. Koornwinder, The Clebsch-Gordan coefficients for the quantum group S_μU(2) and q-Hahn polynomials, Nederl. Akad. Wetensch. Proc. Ser. A 92 = Indag. Math. 51 (1989), 443-456; MR 91c:17009.

• T.H. Koornwinder, Meixner-Pollaczek polynomials and the Heisenberg algebra, J. Math. Phys. 30 (1989), 767-769; MR 90e:33037.

1988

• T.H. Koornwinder, Group theoretic interpretations of Askey's scheme of hypergeometric orthogonal polynomials, in Orthogonal polynomials and their applications, Lecture Notes in Math. 1329, Springer-Verlag, 1988, pp. 46-72;  MR0973421;  also at CWI repository.

• B. Hoogenboom and T.H. Koornwinder, Fonctions d'entrelacement sur les groupes de Lie compacts et polynômes orthogonaux de plusieurs variables, in Séminaire d'Analyse Harmonique, Ecole d'été, 1984, Faculté des Sciences de Tunis, Département de Mathématiques, 1988, pp. 78-93; preprint Report PM-R8601 (downloadable), CWI, Amsterdam, 1986.

1986

• T.H. Koornwinder, A group theoretic interpretation of Wilson polynomials, in Complex analysis and applications '85, Publishing House of the Bulgarian Academy of Sciences, Sofia, 1986, pp. 335-355; MR 89h:33019; also preprint Report PM-R8504 (downloadable), CWI, Amsterdam, 1985; see errata to the preprint version (pdf).

• T.H. Koornwinder, A group theoretic interpretation of the last part of de Branges' proof of the Bieberbach conjecture, Complex Variables Theory Appl. 6 (1986), 309-321; pdf at CWI repository; MR0871737.

• R. Askey, T.H. Koornwinder and M. Rahman, An integral of products of ultraspherical functions and a q-extension, J. London Math. Soc. (2) 33 (1986), 133-148; MR0829394.

1985

• T.H. Koornwinder, Matrix elements of irreducible representations of SU(2) x SU(2) and vector-valued orthogonal polynomials, SIAM J. Math. Anal. 16 (1985), 602-613; MR 86j:22017.

• T.H. Koornwinder, Special orthogonal polynomial systems mapped onto each other by the Fourier-Jacobi transform, in Polynômes orthogonaux et applications, Lecture Notes in Math. 1171, Springer-Verlag, 1985, pp. 174-183;  MR0838982;  also preprint Report PM-R8501, CWI, Amsterdam, 1985. See errata and comments (last modified 26 April 2021).

1984

• T.H. Koornwinder, Orthogonal polynomials with weight function
  (1-x)^α(1+x)^β+Mδ(x+1)+Nδ(x-1), Canad. Math. Bull. 27 (1984), 205-214;  MR0740416.
  See comments (last modified 24 July 2023).

• T.H. Koornwinder and J.J. Lodder, Generalised functions as linear functionals on generalized functions, in: Anniversary volume on approximation theory and functional analysis (Oberwolfach, 1983), Internat. Schriftenreihe Numer. Math. 65, Birkhäuser, Basel, 1984, pp. 151-163; MR 87g:46067; download pdf.

• T.H. Koornwinder, Jacobi functions and analysis on noncompact semisimple Lie groups, in Special functions: Group theoretical aspects and applications, R.A. Askey, T.H. Koornwinder and W. Schempp (eds.), Reidel, Dordrecht, 1984, pp. 1-85; MR0774055; pdf of scan (made by Claire-Marie Auger, 44.4 MB); see also errata (last modified March 7, 2013).

• T.H. Koornwinder, Squares of Gegenbauer polynomials and Milin type inequalities, Report PM-R8412, Centre for Math. and Computer Science, Amsterdam, 1984.

1983

• R. Brummelhuis and T.H. Koornwinder, The generalized Abel transform for SL(2,C), in Topics in modern harmonic analysis, Vol. I, Istituto Nazionale di Alta Matematica Francesco Severi, Roma, 1983, pp. 405-444; MR 85i:22021; download pdf.

• P.C. Greiner and T.H. Koornwinder, Variations on the Heisenberg spherical harmonics, Report ZW 186/83, Mathematisch Centrum, Amsterdam, 1983;
  download pdf.

1982

• T.H. Koornwinder, The representation theory of SL(2,R), a non-infinitesimal approach, Enseign. Math. (2) 38 (1982), 53-87; MR 84e:22016.

• T.H. Koornwinder, A note on the multiplicity free reduction of certain orthogonal and unitary groups, Nederl. Akad. Wetensch. Proc. Ser. A 85 = Indag. Math. 44 (1982), 215-218;  MR 84b:22024.

• T.H. Koornwinder, Krawtchouk polynomials, a unification of two different group theoretic interpretations, SIAM J. Math. Anal. 13 (1982), 1011-1023; MR 84f:33022.

• T.H. Koornwinder, Real semisimple Lie algebras, in The structure of real semisimple Lie groups, T.H. Koornwinder (ed.), MC Syllabus 49, Math. Centrum, Amsterdam, 1982, pp. 1-23; MR 84h:22035.

1981

• T.H. Koornwinder, Clebsch-Gordan coefficients for SU(2) and Hahn polynomials, Nieuw Arch. Wisk. (3) 29 (1981), 140-155;  MR0641673;  Zbl 0483.20027;  download pdf;  see errata.

• T.H. Koornwinder, Invariant differential operators on nonreductive homogeneous spaces, Report ZW 153/81, Mathematisch Centrum, Amsterdam, 1981; MR 82g:43011; arXiv:math.RT/0008116.

1980

• T.H. Koornwinder, A precise definition of separation of variables, in Geometrical approaches to differential equations, R. Martini (ed.), Lecture Notes in Math. 810, Springer-Verlag, 1980, pp. 240-263;   MR0589212.

• T.H. Koornwinder, The representation theory of SL(2,R), a global approach, Report ZW 145/80, Mathematisch Centrum, Amsterdam, 1980.

1979

• M. Flensted-Jensen and T.H. Koornwinder, Jacobi functons: the addition formula and the positivity of the dual convolution structure, Ark. Mat. 17 (1979), 139-151;  MR0543509;  download pdf.

• M. Flensted-Jensen and T.H. Koornwinder, Positive definite spherical functions on a non-compact rank one symmetric space, in Analyse harmonique sur les groupes de Lie, II, P. Eymard, J. Faraut, G. Schiffman and R. Takahashi (eds.), Lecture Notes in Math. 739, Springer, 1979, pp. 249-282; MR0560841;  see also errata.

• T.H. Koornwinder, Lie groups and Lie algebras, in Representations of locally compact groups with applications, T.H. Koornwinder (ed.), MC Syllabus 38, Math. Centrum, Amsterdam, 1979, pp. 97-156; MR 81k:22001.

• T.H. Koornwinder, General representation theory, in Representations of locally compact groups with applications, T.H. Koornwinder (ed.), MC Syllabus 38, Math. Centrum, Amsterdam, 1979, pp. 243-279; MR 81k:22001.

• T.H. Koornwinder, Representations of locally compact abelian groups, in Representations of locally compact groups with applications, T.H. Koornwinder (ed.), MC Syllabus 38, Math. Centrum, Amsterdam, 1979, pp. 281-327; MR 81k:22001.

• T.H. Koornwinder and H.A. van der Meer, Induced representations of locally compact groups, in Representations of locally compact groups with applications, T.H. Koornwinder (ed.), MC Syllabus 38, Math. Centrum, 1979, pp. 329-376; MR 81k:22001.

1978

• T.H. Koornwinder and I.G. Sprinkhuizen, Generalized power series expansions for a class of orthogonal polynomials in two variables, SIAM J. Math. Anal. 9 (1978), 457-483; MR 58 #12170.

• T.H. Koornwinder and I. Sprinkhuizen-Kuyper, Hypergeometric functions of 2x2 matrix argument are expressible in terms of Appell's function F₄, Proc. Amer. Math. Soc. 70 (1978), 39-42; MR 57 #12926.

• T.H. Koornwinder, Positivity proofs for linearization and connection coefficients of orthogonal polynomials satisfying an addition formula, J. London Math. Soc. (2) 18 (1978), 101-114;  MR0493144.

• R. Askey, M.E.H. Ismail and T.H. Koornwinder, Weighted permutation problems and Laguerre polynomials, J. Combin. Theory Ser. A 25 (1978), 226-241; MR 80b:33004.

1977

• T.H. Koornwinder, Yet another proof of the addition formula for Jacobi polynomials, J. Math. Anal. Appl. 61 (1977), 136-141; MR 56 #16020.

• T.H. Koornwinder, The addition formula for Laguerre polynomials, SIAM J. Math. Anal. 8 (1977), 535-540; MR 56 #12357.

• T. Koornwinder, Harmonics and spherical functions on Grassmann manifolds of rank two and two-variable analogues of Jacobi polynomials, in Constructive theory of functions of several variables, W. Schempp and K. Zeller (eds.), Lecture Notes in Math. 571, Springer-Verlag, 1977, pp. 141-154; MR0486701.

1976

• T.H. Koornwinder, A note on the absolute bound for systems of lines, Nederl. Akad. Wetensch. Proc. Ser. A 79 = Indag. Math. 38 (1976), 152-153; MR 53 #7977.

• T.H. Koornwinder, The topological degree of a mapping, in Nonlinear analysis, Vol. I, N.M. Temme (ed.), MC Syllabus 26.1, Math. Centrum, Amsterdam, 1976, pp. 7-39; MR 58 #12531a.

• T.H. Koornwinder, Examination of stability by means of Lyapunov functions, in Nonlinear diffusion problems, O. Diekmann and N.M. Temme (eds.), MC Syllabus 28, Amsterdam, 1976, pp. 136-164.

1975

• T. Koornwinder, A new proof of a Paley-Wiener type theorem for the Jacobi transform, Ark. Mat. 13 (1975), 145-159;  MR0374832 ; see errata.

• T. Koornwinder, Two-variable analogues of the classical orthogonal polynomials, in: Theory and application of special functions, R.A. Askey (ed.), Academic Press, 1975, pp. 435-495; MR 53 #5967; pdf of scan.

• T. Koornwinder, Jacobi polynomials, III. An analytic proof of the addition formula, SIAM J. Math. Anal. 6 (1975), 533-543;  MR0447656;  download pdf.

• T.H. Koornwinder, New proof of the positivity of generalized translation for Jacobi series, part 3 of Three notes on classical orthogonal polynomials, report TW 150/75, Mathematisch Centrum, Amsterdam, 1975; pdf of scan.

1974

• T. Koornwinder, Jacobi polynomials, II. An analytic proof of the product formula, SIAM J. Math. Anal. 5 (1974), 125-137;  MR0385198; download pdf.

• T.H. Koornwinder, Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators, I, II, Nederl. Akad. Wetensch. Proc. Ser. A 77 = Indag. Math. 36 (1974), 48-58, 59-66; download journal article: part I, part II;   MR 49 #5425a, #5425b.

• T.H. Koornwinder, Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators, III, IV, Nederl. Akad. Wetensch. Proc. Ser. A 77 = Indag. Math. 36 (1974), 357-369, 370-381; download journal article: part III, part IV;   MR 50 #10371a, #10371b,  see errata (last modified 14 September 2018).

• T.H. Koornwinder, The addition formula for Jacobi polynomials and the theory of orthogonal polynomials in two variables, a survey, Report TW 145/74, Math. Centrum, Amsterdam, 1974.

1973

• M. Flensted-Jensen and T. Koornwinder, The convolution structure for Jacobi function expansions, Ark. Mat. 11 (1973), 245-262;  MR0340938;  download pdf.

• T. Koornwinder, The addition formula for Jacobi polynomials and spherical harmonics, SIAM J. Appl. Math. 25 (1973), 236-246;  MR0346212.

• T. Koornwinder, Explicit formulas for special functions related to symmetric spaces, Proc. Sympos. Pure Math. 26 (1973), 351-354;  MR0346211;  download pdf.

1972

• T.H. Koornwinder, The addition formula for Jacobi polynomials I. Summary of results, Nederl. Akad. Wetensch. Proc. Ser. A 75 = Indag. Math. 34 (1972), 188-191;  MR0308476.

• T.H. Koornwinder, The addition formula for Jacobi polynomials II. The Laplace type integral and the product formula, Report TW 133/72. Mathematisch Centrum, Amsterdam, 1972,
  2+29 pp.

• T.H. Koornwinder, The addition formula for Jacobi polynomials III. Completion of the proof, Report TW 135/72. Mathematisch Centrum, Amsterdam, 1972, 2+11 pp.

1971

• A. Dijksma and T.H. Koornwinder, Spherical harmonics and the product of two Jacobi polynomials, Nederl. Akad. Wetensch. Proc. Ser. A 74 = Indag. Math. 33 (1971), 191-196;  MR0291519.

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