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Research publications

  1. Erik Koelink, Pablo Román, Wadim Zudilin, An evolution of matrix-valued orthogonal polynomials, arXiv:2411.18362
  2. Erik Koelink, Pablo Román, Wadim Zudilin, A partial-sum deformation for a family of orthogonal polynomials, Indagationes Math (to appear), arXiv:2409.00261
  3. Erik Koelink, Lucía Morey, Pablo Román, Matrix exceptional Laguerre polynomials, Studies in Applied Mathematics 152 (2024), 778-809.
  4. Erik Koelink, Jie Liu, BC2 type multivariable matrix functions and matrix spherical functions, Publ. Res. Inst. Math. Sci. 60 (2024), 305-349.
  5. Wolter Groenevelt, Erik Koelink, Orthogonal functions related to Lax pairs in Lie algebras, Ramanujan Journal 61 (2023), 445-474.
  6. Erik Koelink, Henrique Tyrrell, Non-extremal weight modules for quantized universal enveloping algebras, Indagationes Mathematicae 31 (2020), 458-476.
  7. Erik Koelink, Jean-Michel Lemay, Luc Vinet, Convolution identities for Dunkl orthogonal polynomials from the osp(1|2) Lie superalgebra, Journal of Mathematical Physics 60 (2019), 091701.
  8. Mourad E.H. Ismail, Erik Koelink, Pablo Román, Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice, Advances in Applied Mathematics 110 (2019), 235-269.
  9. Erik Koelink, Pablo Román, Matrix valued Laguerre polynomials, pp. 295-320 in ``Positivity and Noncommutative Analysis Festschrift in Honour of Ben de Pagter'' (eds. G. Buskes, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven and A. Wickstead), Birkhäuser, 2019.
  10. Geoffroy Bergeron, Erik Koelink, Luc Vinet, SUq(3) corepresentations and bivariate q-Krawtchouk polynomials, Journal of Mathematical Physics 60 (2019), 051701.
  11. Mourad E.H. Ismail, Erik Koelink, Pablo Román, Generalized Burchnall-type identities for orthogonal polynomials and expansions, SIGMA 14 (2018), 072, 24 pages.
  12. Erik Koelink, Maarten van Pruijssen, Pablo Román, Matrix elements of irreducible representations of SU(n+1) x SU(n+1) and multivariable matrix-valued orthogonal polynomials, Journal of Functional Analysis 278 (2020), 108411.
  13. Erik Koelink, Applications of spectral theory to special functions, pp. 131-212 in ``Lectures on Orthogonal Polynomials and Special Functions'' (ed. H.S. Cohl, M.E.H. Ismail), Lecture Notes of the London Math. Soc. 464, Cambridge U. Press, 2021.
  14. Noud Aldenhoven, Erik Koelink, Pablo Román, Branching rules for finite-dimensional $\mathcal{U}_q(\mathfrak{su}(3))$-representations with respect to a right coideal subalgebra, Algebras and Representation Theory 20 (2017), 821-842.
  15. Erik Koelink, Pablo Román, Orthogonal vs. non-orthogonal reducibility of matrix-valued measures, SIGMA 12 (2016), 008, 9 pages.
  16. Noud Aldenhoven, Erik Koelink, Pablo Román, Matrix-valued orthogonal polynomials related to the quantum analogue of (SU(2) x SU(2),diag), Ramanujan Journal (2017) 43, 243-311. Accompanying computer algebra package (as tar.gz) in sage available. (Use right-click and choose "Save Target As..." or "Save Link As..." to obtain the file.)
  17. Teun Dings, Erik Koelink, On the Mathieu Conjecture for SU(2), Indagationes Mathematicae 26 (2015), 219-224.
  18. Erik Koelink, Ana M. de los Ríos, Pablo Román, Matrix-valued Gegenbauer-type polynomials, Constructive Approximation 46 (2017), 459-487. Accompanying Maple worksheet available. (Use right-click and choose "Save Target As..." or "Save Link As..." to obtain the worksheet.)
  19. Kenny De Commer, Erik Koelink, A q-Hankel transform associated to the quantum linking groupoid for the quantum SU(2) and E(2) groups, Proceedings of the American Mathematical Society 143 (2015), 2515-2526.
  20. Noud Aldenhoven, Erik Koelink, Ana M. de los Ríos, Matrix-valued little q-Jacobi polynomials, Journal of Approximation Theory 193 (2015), 164-183.
  21. Wolter Groenevelt, Erik Koelink, A hypergeometric function transform and matrix-valued orthogonal polynomials, Constructive Approximation 38 (2013), 277-309.
  22. Wolter Groenevelt, Mourad E.H. Ismail, Erik Koelink, Spectral theory and matrix-valued orthogonal polynomials, Advances in Mathematics 244 (2013), 91-105.
  23. Erik Koelink, Maarten van Pruijssen, Pablo Román, Matrix valued orthogonal polynomials related to (SU(2) x SU(2), diag), II, Publications of the Research Institute for Mathematical Sciences 49, no. 2, (2013), 271-312.
  24. Mourad E.H. Ismail, Erik Koelink, Spectral analysis of certain Schrödinger operators, SIGMA 8 (2012), 061, 19 pages.
  25. Mourad E.H. Ismail, Erik Koelink, Spectral properties of operators using tridiagonalisation, Analysis and Applications 10, no. 3, (2012), 327-343.
  26. Erik Koelink, Maarten van Pruijssen, Pablo Román, Matrix Valued Orthogonal Polynomials related to (SU(2) x SU(2),diag), International Mathematics Research Notices 2012, no. 24, 5673-5730.
  27. Martijn Caspers, Erik Koelink, Modular properties of matrix coefficients of corepresentations of a locally compact quantum group, Journal of Lie Theory 21, no. 4, (2011), 905-928.
  28. Wolter Groenevelt, Erik Koelink, The indeterminate moment problem for the q-Meixner polynomials, Journal of Approximation Theory 163, no. 7, (2011), 838-863.
  29. Wolter Groenevelt, Erik Koelink, Johan Kustermans, The dual quantum group for the quantum group analogue of the normalizer of SU(1,1) in SL(2,C), International Mathematics Research Notices (2010) 2010, no. 7, 1167-1314 (doi:10.1093/imrn/rnp173) In case you are only interested in the section on identities for special functions, click here.
  30. Mourad E.H. Ismail, Erik Koelink, The J-matrix method, Advances in Applied Mathematics 46 (2011), 379-395.
  31. Erik Koelink, Walter Van Assche, Leonhard Euler and a q-analogue of the logarithm, Proceedings of the American Mathematical Society 137 (2009), 1663-1676.
  32. Jacob S. Christiansen, Erik Koelink, Self-adjoint difference operators and symmetric Al-Salam and Chihara polynomials, Constructive Approximation 28 (2008), 199-218.
  33. Erik Koelink, Yvette van Norden, The dynamical U(n) quantum group, International Journal of Mathematics and Mathematical Sciences 2006 Art. ID 65279, 30 pp.
  34. Jacob S. Christiansen, Erik Koelink, Self-adjoint difference operators and classical solutions to the Stieltjes-Wigert moment problem, Journal of Approximation Theory 140 (2006), 1-26.
  35. Erik Koelink, Yvette van Norden, Pairings and actions for dynamical quantum groups, Advances in Mathematics 208 (2007), 1-39.
  36. Erik Koelink, One-parameter orthogonality relations for basic hypergeometric series, Indagationes Mathematicae N.S. 14 (2003), 423-443.
  37. Erik Koelink, Yvette van Norden, Hjalmar Rosengren, Elliptic U(2) quantum group and elliptic hypergeometric series, Communications in Mathematical Physics 245 (2004), 519-537.
  38. Wolter Groenevelt, Erik Koelink, Hjalmar Rosengren, Continuous Hahn functions as Clebsch-Gordan coefficients, pp. 221-284 in "Theory and Applications of Special Functions. A Volume Dedicated to Mizan Rahman" (eds. M. E. H. Ismail and E. Koelink), Developments in Mathematics, Vol. 13, Kluwer Academic Publishers, 2005.
  39. Erik Koelink, Johan Kustermans, Quantum SU(1,1) and its Pontryagin dual, 49--77 in ``Locally Compact Quantum Groups and Groupoids'' (ed. L. Vainerman), IRMA Lectures in Mathematics and Theoretical Physics 2, de Gruyter, Berlin, 2003.
  40. Wolter Groenevelt, Erik Koelink, Meixner functions and polynomials related to Lie algebra representations, Journal of Physics. A. Mathematical and Theoretical 35 (2002), no. 1, 65-85.
  41. Erik Koelink, Spectral theory and special functions, 45-84 in `Laredo Lectures on Orthogonal Polynomials and Special Functions' (eds. R. Álvarez-Nodarse, F. Marcellán, W. Van Assche), Nova Science Publishers, 2004.
  42. Erik Koelink, Johan Kustermans, A locally compact quantum group analogue of the normalizer of SU(1,1) in SL(2,C), Commun. Math. Phys. 233 (2003), 231-296.
  43. Erik Koelink, Lie theory and special functions, 289-304 in ``Recent Advances in Lie Theory'' (eds. I. Bajo and E. Sanmartin), Research and Exposition in Mathematics Volume 25, Heldermann Verlag, 2002.
  44. Erik Koelink, Hjalmar Rosengren, Transmutation kernels for the little q-Jacobi function transform, Rocky Mountain Journal of Mathematics 32, no 2, (2002), 703-738.
  45. Erik Koelink, Hjalmar Rosengren, Harmonic analysis on the SU(2) dynamical quantum group, Acta Applicandae Mathematicae 69 (2001), 163-220.
  46. Erik Koelink, Jasper V. Stokman, The Askey-Wilson function transform, International Mathematical Research Notices 22 (2001), 1203-1227.
  47. Erik Koelink, Jasper V. Stokman, The Askey-Wilson function transform scheme, pp. 221-241 in ``Special Functions 2000: Current Perspective and Future Directions'' (eds. J. Bustoz, M.E.H. Ismail, S.K. Suslov), NATO Science Series II, Vol. 30, Kluwer, 2001.
  48. Erik Koelink, Jasper V. Stokman, with an appendix by Mizan Rahman, Fourier transforms on the quantum SU(1,1) group, Publications of the Research Institute for Mathematical Sciences 37 (2001), 621-715.
  49. Erik Koelink, Jasper V. Stokman, The big q-Jacobi function transform, Constructive Approximation 19 (2003), 191-235.
  50. Nicola Ciccoli, Erik Koelink, Tom H. Koornwinder, q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations, Methods and Applications of Analysis 6 (1999), 109-127.
  51. H.T. Koelink, Some basic Lommel polynomials, Journal of Approximation Theory 96 (1999), 345-365.
  52. H.T. Koelink, J. Van der Jeugt, Bilinear generating functions for orthogonal polynomials, Constructive Approximation 15 (1999), 481-497.
  53. H.T. Koelink, J. Van der Jeugt, Convolutions for orthogonal polynomials from Lie and quantum algebra representations, SIAM Journal on Mathematical Analysis 29 (1998), 794-822.
  54. H.T. Koelink, q-Krawtchouk polynomials as spherical functions on the Hecke algebra of type B, Transactions of the American Mathematical Society 352 (2000), no. 10, 4789-4813.
  55. P.G.A. Floris, H.T. Koelink, A commuting q-analogue of the addition formula for disk polynomials, Constructive Approximation 13 (1997), 511-535.
  56. Erik Koelink, Convolution and addition theorems for q-orthogonal polynomials, Proc. Intern. Workshop on Orthogonal Polynomials 1996 (eds. M. Alfaro, R. Álvarez-Nodarse, G. López Lagomasino and F. Marcellán), Madrid 1997, 113-122.
  57. Erik Koelink, Addition formulas for q-special functions, `Special Functions, q-Series and Related Topics' (eds. M.E.H. Ismail, D.R. Masson, M. Rahman), Fields Institute Communications 14, AMS, 1997, 109-129.
  58. H.T. Koelink, J. Verding, Spectral analysis and the Haar functional on the quantum SU(2) group, Communications in Mathematical Physics 177 (1996), 399-415.
  59. H.T. Koelink, On Jacobi and continuous Hahn polynomials, Proceedings of the American Mathematical Society 124 (1996), 887-898.
  60. H.T. Koelink, Yet another basic analogue of Graf's addition formula, Journal of Computational and Applied Mathematics 68 (1996), 209-220.
  61. Erik Koelink, 8 Lectures on quantum groups and q-special functions, Revista Colombiana de Matemáticas 30:2, 93-180 (1996).
  62. H.T. Koelink, Askey-Wilson polynomials and the quantum SU(2) group: survey and applications, Acta Applicandae Mathematicae 44 (1996), 295-352.
  63. H.T. Koelink, W. Van Assche, Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function, Constructive Approximation 11 (1995), 477-512.
  64. H.T. Koelink, The quantum group of plane motions and basic Bessel functions, Indagationes Mathematicae N.S. 6 (1995), 197-211.
  65. H.T. Koelink, Identities for q-ultraspherical polynomials and Jacobi functions, Proceedings of the American Mathematical Society 123 (1995), 2479-2487.
  66. H.T. Koelink, R.F. Swarttouw, A q-analogue of Graf's addition formula for the Hahn-Exton q-Bessel function, Journal of Approximation Theory 81 (1995), 260-273.
  67. H.T. Koelink, Addition formula for big q-Legendre polynomials from the quantum SU(2) group, Canadian Journal of Mathematics 47 (1995), 436-448.
  68. H.T. Koelink, The quantum group of plane motions and the Hahn-Exton q-Bessel function, Duke Mathematical Journal 76 (1994), 483-508.
  69. H.T. Koelink, A basic analogue of Graf's addition formula and related formulas, Integral Transforms and Special Functions 1 (1993), 165-182.
  70. H.T. Koelink, R.F. Swarttouw, On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials, Journal of Mathematical Analysis and Applications 186 (1994), 690-710.
  71. H.T. Koelink, H. Schippers, J.J. Heijstek, J.J. Derksen, Modal analysis of solar panels using boundary integral equations, pp. 515--525 in ``Boundary Elements XIV, Volume 2: Stress Analysis and Computational Aspects'', (eds. C.A. Brebbia, J. Dominguez and F. Paris), Comput. Mech. Publications and Elsevier Science Publ., 1992.
  72. H.T. Koelink, Hansen-Lommel orthogonality relations for Jackson's q-Bessel functions, Journal of Mathematical Analysis and Applications 175 (1993), 425-437.
  73. H.T. Koelink, Quantum group theoretic derivation of the addition formula for continuous q-Legendre polynomials, Contemporary Mathematics 134 (1992), 139-140.
  74. H.T. Koelink, The addition formula for continuous q-Legendre polynomials and associated spherical elements on the SU(2) quantum group related to Askey-Wilson polynomials, SIAM Journal on Mathematical Analysis 25 (1994), 197-217.
  75. H.Tjerk Koelink, On *-representations of the Hopf *-algebra associated with the quantum group U_q(n), Compositio Mathematica 77 (1991), 199-231.
  76. H.T. Koelink, T.H. Koornwinder, The Clebsch-Gordan coefficients for the quantum group SμU(2) and q-Hahn polynomials, Indagationes Mathematicae 51 (1989), 443-456.

Editorial

Books

  1. Erik Koelink, Stefan Kolb, Nicolai Reshetikhin, Bart Vlaar (eds.), Hypergeometry, Integrability and Lie Theory, Contemporary Mathematics, vol. 780, Amer. Math. Soc., 2022. (347 pp; Softcover, ISBN: 978-1-4704-6520-9)
  2. Erik Koelink, Jan van Neerven, Ben de Pagter, Guido Sweers (eds.), Partial Differential Equations and Functional Analysis (The Philippe Clément Festschrift), Operator Theory: Advances and Applications 168, Birkhäuser, 2006 (VI, 294 p., Hardcover ISBN: 3-7643-7600-7).
  3. Mourad E. H. Ismail, Erik Koelink (eds.), Theory and Applications of Special Functions. A Volume Dedicated to Mizan Rahman, Developments in Mathematics, Vol. 13, Kluwer Academic Publishers, 2005, XVI, 491p., Hardcover ISBN: 0-387-24231-7.
  4. Erik Koelink, Walter Van Assche (eds.), Orthogonal Polynomials and Special Functions: Leuven 2002, Lecture Notes in Mathematics 1817, Springer Verlag, 2003 (X, 249 p. Softcover 3-540-40375-2).

Journals

  1. Constructive Approximation (editorial board since 2002)
  2. Advances in Applied Mathematics (editorial board since 2011)
  3. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) (editorial board since 2013)
  4. Journal of Approximation Theory (editorial board since 2014)
  5. Journal of Physics A (advisory board 2008-2010)
  6. guest editor (with Marcel de Jeu, Eric Opdam, Misha Pevzner) for special issue Indagationes Mathematicae, New Series 36 (1,2) (2025) dedicated to the memory of Gerrit van Dijk (1939-2022).
  7. guest editor (with Peter Clarkson, Ana Loureiro, Walter Van Assche) of a Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14) for SIGMA (2017/2018)
  8. guest editor (with Nalini Joshi, Tom Koornwinder, Masatoshi Noumi, Simon Ruijsenaars, Fedor Smirnov, Jasper Stokman) of a special issue on the Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems for SIGMA (2010/2011).
  9. guest editor (with Mourad Ismail, Victor Reiner) for a special issue Advances in Applied Mathematics 46 (2011) for Dennis Stanton's 60th birthday.
  10. guest editor (with Marcel de Jeu, Eric Opdam, Misha Pevzner) for special issue Indagationes Mathematicae, New Series 16 (3,4) (2005), on the occasion of the retirement of Gerrit van Dijk.
  11. guest editor (with Eric Opdam, Jasper Stokman, Nico Temme, Jan Wiegerinck) for special issue Indagationes Mathematicae, New Series 14 (3,4) (2003), on the occasion of Tom Koornwinder's 60th birthday.

Miscellaneous publications

  1. Wolter Groenevelt, Erik Koelink, Mizan Rahman, Basic Hypergeometric Series, chapter to appear in one of the volumes of the Askey-Bateman Project (eds. Mourad Ismail and Walter Van Assche), Cambridge Univ. Press, to appear.
  2. Erik Koelink, Review of ``Encyclopedia of Special Functions: The Askey-Bateman Project, Volume II Multivariable Special Finctions'' edited by Tom H. Koornwinder, Jasper V. Stokman, Nieuw Archief voor Wiskunde vijfde serie 24 (2023), 121-122.
  3. Mourad E.H. Ismail, Erik Koelink, In memoriam: Mizan Rahman, Journal of Approximation Theory 201 (2016), 87-97.
  4. Erik Koelink (joint with Noud Aldenhoven, Pablo Román), Matrix-valued orthogonal polynomials associated to an explicit quantum symmetric pair, p. 546-7 in Oberwolfach Reports 12 (1), 2015.
  5. Erik Koelink, Stefan Kolb, Review of ``Quantum bounded symmetric domains'' by Leonid L. Vaksman, Bulletin of the American Mathematical Society 50 (2013), 337-345.
  6. Erik Koelink, Review of ``Classical and quantum orthogonal polynomials in one variable'' by Mourad E.H. Ismail, Bulletin of the London Mathematical Society 43 (2011), 615-617.
  7. Mourad E.H. Ismail, Erik Koelink, Victor Reiner, A tribute to Dennis Stanton, Advances in Applied Mathematics 46 (2011), 1-14.
  8. Erik Koelink, Review of ``Orthogonal polynomials and continued fractions'' by S. Khruschev, Nieuw Archief voor Wiskunde vijfde serie 11 (2010), 217, (in Dutch).
  9. Erik Koelink, Review of ``Quantum Groups. A path to current algebra'' by Ross Street, Nieuw Archief voor Wiskunde vijfde serie 10 (2009), 282, (in Dutch).
  10. Erik Koelink, Review of ``Analysis I, II'' by Terence Tao, Nieuw Archief voor Wiskunde vijfde serie 9 (2008), 219-220, (in Dutch).
  11. Erik Koelink, Grensoverschrijdende wiskunde, oratie Radboud Universiteit Nijmegen, 5 juni 2008.
  12. Erik Koelink, Review of ``The dynamical Yang-Baxter equation, Representation Theory, and Quantum Integrable Systems'' by Pavel Etingof and Frederic Latour, Nieuw Archief voor Wiskunde vijfde serie 8 (2007), 303--304 (in Dutch).
  13. Erik Koelink, Review of ``Lie algebras of finite and affine type'' by Roger Carter, Contemporary Physics 48 (4),2007.
  14. Erik Koelink, Review of ``Classical and quantum orthogonal polynomials in one variable.'' by Mourad E.H. Ismail, SIAM Review 48 (2006), 804-805.
  15. Richard Askey, Mourad E.H. Ismail, Erik Koelink Mizan Rahman, his mathematics and literary writings, pp. 1-28 in "Theory and Applications of Special Functions. A Volume Dedicated to Mizan Rahman" (eds. M. E. H. Ismail and E. Koelink), Developments in Mathematics, Vol. 13, Kluwer Academic Publishers, 2005.
  16. Erik Koelink, Review of ``Basic Hypergeometric Series, 2nd ed.'' by George Gasper and Mizan Rahman, Nieuw Archief voor Wiskunde vijfde serie 6 (2005), 329--330.
  17. Erik Koelink, Review of ``Matrix Groups: An Introduction to Lie Group Theory'' by Andrew Baker, Nieuw Archief voor Wiskunde vijfde serie 4 (2003), 338, (in Dutch).
  18. H.T. Koelink, Review of ``Quantum Groups and Lie Theory'' edited by Andrew Pressley Contemporary Physics 44 (2003), 182-183.
  19. Erik Koelink, Review of ``Time-frequency Representations'' by R.Tolimieri and M. An, Nieuw Archief voor Wiskunde vijfde serie 1 (2000), 95-96. (in Dutch)
  20. Erik Koelink, Tom H. Koornwinder, Review of ``Representation of Lie Groups and Special Functions, Vols. 1,2,3'' by N.Ja. Vilenkin and A.U. Klimyk, Kluwer, 1991, 1992, 1992, Bull. Amer. Math. Soc. 35 (1998), 265-270.
  21. H.T. Koelink, T.H. Koornwinder, Addition theorems in the theory of special functions, Encyclopaedia of Mathematics Supplement Volume I, Kluwer Acad. Publ., 1997, p. 29.
  22. Erik Koelink, Book review of ``Lectures on Hermite and Laguerre expansions'' by Sundaram Thangavelu, Bull. Belgian Math. Soc./Simon Stevin 1 (1994), 581-582.
  23. H.T. Koelink, T.H. Koornwinder, q-special functions, a tutorial, Contemp. Math. 134 (1992), 141-142.

Lecture notes (unpublished)

  1. Erik Koelink, Commutative triples in group representations and special functions, lecture notes for course NWI-WM116B Advanced Topics in Representation Theory (2022/2023) and for winter school ``Harmonic analysis and special functions in mathematical physics'' (31/7-4/8 2023, Córdoba, Argentina).
  2. Erik Koelink, Analysis 1, 2023.
  3. Erik Koelink, q-special functions, basic hypergeometric series and operators, lecture notes OPSFA Summer School 2018, Sousse, Tunisia. Lecture notes available.
  4. Martijn Caspers, Erik Koelink, Quantum groups and special functions, course Faculté des Sciences de Bizerte, Tunisia, February 22-27, 2010.
  5. Erik Koelink, Scattering Theory, 2008 (with minor corrections 2018)
  6. Erik Koelink, Eindige groepen van Lie type (in Dutch), 1998.

Non-published research publications

  1. H.T. Koelink, Addition formula for 2-parameter family of Askey-Wilson polynomials, preprint Katholieke Universiteit Leuven, 1994, pp. 1-16.
  2. H.T. Koelink, On q-Bessel functions related to the quantum group of plane motions, report W-91-26, University of Leiden, 1991, pp. 1-51.
  3. H.T. Koelink, ``On quantum groups and q-special functions'', thesis, University of Leiden, 1991, pp. 1-124.
  4. Erik Koelink, Leo Westermann, Chebychev measure for the deviation from linearity, Research Memorandum nr. 222, Institute of Economic Research, Faculty of Economics, University of Groningen, 1987, pp. 1-21.
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