- 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.
- H.T. Koelink, On *-representations of the
Hopf *-algebra associated with the quantum group U_q(n),
Compos. Math. 77 (1991), 199-231.
- 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.
- H.T. Koelink, Quantum group
theoretic derivation of the
addition formula for continuous q-Legendre polynomials,
Contemp. Math. 134 (1992), 139-140.
- H.T. Koelink, Hansen-Lommel orthogonality
relations for Jackson's q-Bessel functions,
J. Math. Anal. Appl. 175 (1993), 425-437.
- 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.
- 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.
- H.T. Koelink, A basic analogue of Graf's
addition formula and related formulas,
Integral Transf. and Special Funct. 1 (1993),
165-182.
- H.T. Koelink, The quantum group of plane motions
and the Hahn-Exton q-Bessel function, Duke Math. J. 76
(1994), 483-508.
- H.T. Koelink, Addition formula for
big q-Legendre polynomials from the quantum SU(2) group,
Canad. J. Math. 47 (1995), 436-448.
- 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.
- H.T. Koelink, Identities for q-ultraspherical
polynomials and Jacobi functions, Proc. Amer.
Math. Soc. 123 (1995), 2479-2487.
- H.T. Koelink, The quantum group of plane motions
and basic Bessel functions,
Indag. Mathem. N.S. 6 (1995), 197-211.
- 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.
- H.T. Koelink, Askey-Wilson polynomials and the
quantum SU(2) group: survey and applications,
Acta Appl. Math. 44 (1996), 295-352.
- 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)
- H.T. Koelink, Yet another basic analogue of Graf's addition formula,
J. Comput. Appl. Math. 68 (1996), 209-220.
- H.T. Koelink, On Jacobi and continuous Hahn polynomials,
Proc. Amer. Math. Soc.
124 (1996), 887-898.
- 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.
- 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.
- 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.
-
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.
- 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.
- 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.
- H.T. Koelink and
J. Van der Jeugt, Bilinear generating functions for
orthogonal polynomials,
Constructive Approximation 15 (1999),
481-497.
- H.T. Koelink,
Some basic Lommel polynomials,
J. Approx. Theory 96 (1999), 345-365.
- 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.
- Erik Koelink and Jasper V. Stokman,
The big q-Jacobi function
transform, Constructive Approximation 19
(2003), 191-235.
- 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.
- 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.
- Erik Koelink and Jasper V. Stokman,
The Askey-Wilson function
transform, Intern. Math. Res. Notices 22
(2001), 1203-1227.
- Erik Koelink and Hjalmar Rosengren,
Harmonic analysis on
the SU(2) dynamical quantum group, Acta Applic. Math.
69 (2001), 163-220.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- Erik Koelink,
One-parameter orthogonality relations for basic
hypergeometric series, Indagationes Mathematicae N.S.
14 (2003), 423-443. See also
math.CA/0305385
- 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
- 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.
- 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
- Jacob S. Christiansen and Erik Koelink,
Self-adjoint difference
operators and symmetric
Al-Salam and Chihara polynomials,
preprint
math.CA/0610534
Books
- 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.
- 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.
- 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).
- 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.
- H.T. Koelink, ``On quantum groups and
q-special functions'', thesis,
University of Leiden, 1991, pp. 1-124.
- 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.
- 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.
- H.T. Koelink and T.H. Koornwinder,
q-special functions, a tutorial,
Contemp. Math.
134 (1992), 141-142.
- Erik Koelink, Book review of ``Lectures on
Hermite and Laguerre expansions'' by Sundaram Thangavelu,
Bull. Belgian Math. Soc./Simon Stevin 1 (1994),
581-582.
- 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.
- 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.
- 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)
- H.T. Koelink, Review of
``Quantum Groups and Lie Theory''
edited by Andrew Pressley
Contemporary Physics 44 (2003), 182-183.
- 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).
- Erik Koelink,
Review of ``Basic Hypergeometric Series, 2nd ed.''
by George Gasper and Mizan Rahman,
Nieuw Archief voor Wiskunde vijfde serie
to appear.
- 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.
- Erik Koelink,
Review of ``Classical and quantum orthogonal polynomials in one variable.''
by Mourad E.H. Ismail,
SIAM Review 48 (2006), 804-805.
- 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).