Research publications


  1. H.T. Koelink and T.H. Koornwinder, The Clebsch-Gordan coefficients for the quantum group S_{\mu}U(2) and q-Hahn polynomials, Indag. Mathem. 51 (1989), 443-456.
  2. H.T. Koelink, On *-representations of the Hopf *-algebra associated with the quantum group U_q(n), Compos. Math. 77 (1991), 199-231.
  3. 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 J. Math. Anal. 25 (1994), 197-217.
  4. H.T. Koelink, Quantum group theoretic derivation of the addition formula for continuous q-Legendre polynomials, Contemp. Math. 134 (1992), 139-140.
  5. H.T. Koelink, Hansen-Lommel orthogonality relations for Jackson's q-Bessel functions, J. Math. Anal. Appl. 175 (1993), 425-437.
  6. H.T. Koelink, H. Schippers, J.J. Heijstek and 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.
  7. H.T. Koelink and R.F. Swarttouw, On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials, J. Math. Anal. and Appl. 186 (1994), 690-710.
  8. H.T. Koelink, A basic analogue of Graf's addition formula and related formulas, Integral Transf. and Special Funct. 1 (1993), 165-182.
  9. H.T. Koelink, The quantum group of plane motions and the Hahn-Exton q-Bessel function, Duke Math. J. 76 (1994), 483-508.
  10. H.T. Koelink, Addition formula for big q-Legendre polynomials from the quantum SU(2) group, Canad. J. Math. 47 (1995), 436-448.
  11. H.T. Koelink and R.F. Swarttouw, A q-analogue of Graf's addition formula for the Hahn-Exton q-Bessel function, J. Approx. Theory 81 (1995), 260-273.
  12. H.T. Koelink, Identities for q-ultraspherical polynomials and Jacobi functions, Proc. Amer. Math. Soc. 123 (1995), 2479-2487.
  13. H.T. Koelink, The quantum group of plane motions and basic Bessel functions, Indag. Mathem. N.S. 6 (1995), 197-211.
  14. H.T. Koelink and W. Van Assche, Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function, Constr. Approx. 11 (1995), 477-512.
  15. H.T. Koelink, Askey-Wilson polynomials and the quantum SU(2) group: survey and applications, Acta Appl. Math. 44 (1996), 295-352.
  16. Erik Koelink, 8 Lectures on quantum groups and q-special functions, Report 96-10(1996) Universiteit van Amsterdam, 82 pages. The abstract of this paper and the postscript file is available. Revista Colombiana de Matemáticas 30:2, 93-180(1996)
  17. H.T. Koelink, Yet another basic analogue of Graf's addition formula, J. Comput. Appl. Math. 68 (1996), 209-220.
  18. H.T. Koelink, On Jacobi and continuous Hahn polynomials, Proc. Amer. Math. Soc. 124 (1996), 887-898.
  19. H.T. Koelink and J. Verding, Spectral analysis and the Haar functional on the quantum SU(2) group, Commun. Math. Phys. 177 (1996), 399-415.
  20. 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.
  21. Erik Koelink, Convolution and addition theorems for q-orthogonal polynomials, Proc. Intern. Workshop on Orthogonal Polynomials 1996 (eds. M. Alfaro, R. \'Alvarez-Nodarse, G. L\'opez Lagomasino and F. Marcell\'an), Madrid 1997, 113-122.
  22. P.G.A. Floris and H.T. Koelink, A commuting q-analogue of the addition formula for disk polynomials, Constr. Approx. 13 (1997), 511-535.
  23. H.T. Koelink, q-Krawtchouk polynomials as spherical functions on the Hecke algebra of type B, Trans. Amer. Math. Soc. 352 (2000), no. 10, 4789-4813.
  24. H.T. Koelink and J. Van der Jeugt, Convolutions for orthogonal polynomials from Lie and quantum algebra representations, SIAM J. Math. Anal. 29 (1998), 794-822.
  25. H.T. Koelink and J. Van der Jeugt, Bilinear generating functions for orthogonal polynomials, Constructive Approximation 15 (1999), 481-497.
  26. H.T. Koelink, Some basic Lommel polynomials, J. Approx. Theory 96 (1999), 345-365.
  27. Nicola Ciccoli, Erik Koelink and Tom H. Koornwinder, q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations, Methods and Applications of Analysis 6 (1999), 109-127.
  28. Erik Koelink and Jasper V. Stokman, The big q-Jacobi function transform, Constructive Approximation 19 (2003), 191-235.
  29. Erik Koelink and Jasper V. Stokman, with an appendix by Mizan Rahman, Fourier transforms on the quantum SU(1,1) group, Publ. Res. Inst. Math. Sci., Kyoto Univ. 37 (2001), 621-715.
  30. Erik Koelink and 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.
  31. Erik Koelink and Jasper V. Stokman, The Askey-Wilson function transform, Intern. Math. Res. Notices 22 (2001), 1203-1227.
  32. Erik Koelink and Hjalmar Rosengren, Harmonic analysis on the SU(2) dynamical quantum group, Acta Applic. Math. 69 (2001), 163-220.
  33. Erik Koelink and Hjalmar Rosengren, Transmutation kernels for the little q-Jacobi function transform, Rocky Mountain Journal of Mathematics 32, no 2, (2002), 703-738.
  34. 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.
  35. Erik Koelink and 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.
  36. 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.
  37. Wolter Groenevelt and Erik Koelink, Meixner functions and polynomials related to Lie algebra representations, J. Phys. A: Math. Gen. 35 (2002), no. 1, 65-85.
  38. Erik Koelink and 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.
  39. Wolter Groenevelt, Erik Koelink and 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.
  40. Erik Koelink, Yvette van Norden and Hjalmar Rosengren, Elliptic U(2) quantum group and elliptic hypergeometric series , Communications in Mathematical Physics 245 (2004), 519-537. See also math.QA/0304189
  41. Erik Koelink, One-parameter orthogonality relations for basic hypergeometric series, Indagationes Mathematicae N.S. 14 (2003), 423-443. See also math.CA/0305385
  42. Erik Koelink and Yvette van Norden, Pairings and actions for dynamical quantum groups, Advances in Mathematics 208 (2007), 1-39. See also math.QA/0412205
  43. Jacob S. Christiansen and Erik Koelink, Self-adjoint difference operators and classical solutions to the Stieltjes-Wigert moment problem, Journal of Approximation Theory 140 (2006), 1-26, see also math.CA/0504456.
  44. Erik Koelink and Yvette van Norden, The dynamical U(n) quantum group, International Journal of Mathematics and Mathematical Sciences 2006 Art. ID 65279, 30 pp. preprint math.QA/0508168
  45. Jacob S. Christiansen and Erik Koelink, Self-adjoint difference operators and symmetric Al-Salam and Chihara polynomials, preprint math.CA/0610534

Books

  1. Mourad E. H. Ismail and 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. Click here for the publisher's webpage and here for the table of contents.
  2. Erik Koelink and 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). Click here for the publisher's website from which the book is available electronically.
  3. 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).

Non-published research publications


  1. Erik Koelink and 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.
  2. H.T. Koelink, ``On quantum groups and q-special functions'', thesis, University of Leiden, 1991, pp. 1-124.
  3. 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.
  4. H.T. Koelink, Addition formula for 2-parameter family of Askey-Wilson polynomials, preprint Katholieke Universiteit Leuven, 1994, pp. 1-16. The abstract of this paper and the AMS-TeX source file is available.

Miscellaneous publications


  1. H.T. Koelink and T.H. Koornwinder, q-special functions, a tutorial, Contemp. Math. 134 (1992), 141-142.
  2. Erik Koelink, Book review of ``Lectures on Hermite and Laguerre expansions'' by Sundaram Thangavelu, Bull. Belgian Math. Soc./Simon Stevin 1 (1994), 581-582.
  3. H.T. Koelink and T.H. Koornwinder, Addition theorems in the theory of special functions, Encyclopaedia of Mathematics Supplement Volume I, Kluwer Acad. Publ., 1997, p. 29. The postscript file is available.
  4. Erik Koelink and 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.
  5. 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)
  6. H.T. Koelink, Review of ``Quantum Groups and Lie Theory'' edited by Andrew Pressley Contemporary Physics 44 (2003), 182-183.
  7. 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).
  8. Erik Koelink, Review of ``Basic Hypergeometric Series, 2nd ed.'' by George Gasper and Mizan Rahman, Nieuw Archief voor Wiskunde vijfde serie to appear.
  9. Richard Askey, Mourad E.H. Ismail and 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.
  10. Erik Koelink, Review of ``Classical and quantum orthogonal polynomials in one variable.'' by Mourad E.H. Ismail, SIAM Review 48 (2006), 804-805.
  11. 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 to appear (in Dutch).