Walter Van Assche 

Address:

Department of Mathematics
Section of Analysis
Celestijnenlaan 200B
B-3001 Heverlee
BELGIUM
tel: +32-16-327051
fax: +32-16-327998
Email: walter@wis.kuleuven.be

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I am full professor of mathematics at the department of mathematics of the Katholieke Universiteit Leuven. I am currently the head of the department of mathematics and also of the section of Analysis.Up to September 30, 2000 I was a Research Director (onderzoeksdirecteur) of the Belgian National Fund for Scientific Research.

I am an editor of the Journal of Approximation Theory

I am on the editorial board of the Journal of Difference Equations and Applications

I am on the editorial board of the Proceedings of the American Mathematical Society

Research

• Orthogonal polynomials
• Difference equations
• Approximation theory (polynomial approximation, rational approximation, wavelets)
• Mathematical analysis of stochastic processes
• Special functions
• Belgian Interuniversity Attraction Poles Programma P6/02: NOSY Nonlinear Systems, Stochastic Processes and Statistical Mechanics
• Research Grant OT/08/033 of the Research Counsel of K.U.Leuven: Asymptotic analysis of special functions, random matrices and non-intersecting random paths
• FWO project G.0427.09: Asymptotic analysis of non-intersecting Brownian motions

Teaching

• Differentiaalvergelijkingen (Differential Equations), bachelor wiskunde, fysica (bachelor mathematics, physics)
• Differentiaalvergelijkingen, deel 1 (Differential Equations, part 1), bachelor wiskunde, bio-ingenieurswetenschappen (bachelor mathematics, bio-engineering) Campus Kortrijk
• Interpolatie en Approximatie (Interpolation and Approximation), master wiskunde (master mathematics).
• Wiskundige Analyse I (Mathematical Analysis I), bachelor wiskunde (bachelor mathematics), Campus Kortrijk.

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Upcoming Events

• Orthogonal polynomials, special functions and applications (OPSFA 9), CIRM Marseille, France, 2-6 July, 2007 (done)
• Conference on Quantum Probability and Related Topics, Guanajuato, Mexico, 2-8 September, 2007 (with a special session on Interactive Fock Space and Orthogonal Polynomials) (done)
• Random and integrable models in mathematics and physics, Brussels, 11-15 September 2007 (done)
• Special functions, information theory and mathematical physics (in honor of Jesus S. Dehesa), Granada, Spain, 17-19 September, 2007. (done)
• Summer school New trends and directions in harmonic analysis, approximation theory, and image analysis, Inzell, Germany, September 17-21, 2007. (done)
• Joint meeting of the American Mathematical Society and the New Zealand Mathematical Society, Wellington, New Zealand, 12-15 December, 2007. (done)
• 3ème Journées Approximation, Université de Lille, 15-16 May 2008 (done).
• Workshop on Orthogonal Polynomials and Special Functions, Katholieke Universiteit Leuven, 19-20 May 2008 (done).
• Foundations of computational mathematics (FoCM’08), Hong Kong, 16-26 June, 2008 (done).
• Symmetries and integrabilities of difference equations (SIDE 8), Sainte Adele, Canada, 23-29 June, 2008 (done).
• International workshop on orthogonal polynomials and approximation theory (in honor of Guillermo López Lagomasino), Leganés (Madrid), 8-12 September 2008 (done).
• Rolling Waves in Leuven - A workshop on the occasion of Adhemar Bultheel's 60th birthday, Katholieke Universiteit Leuven, 15-16 December 2008. (done)
• Discrete Integrable systems, Isaac Newton Institute for Mathematical Sciences, 19 January – 3 July 2009. (done)
• Quantum integrable discrete systems, 23-27 March 2009, (done)
• Geometric aspects of discrete and ultra-discrete integrable systems, Glasgow, 30 March – 3 April 2009, (done)
• Algebraic theory of difference equations, Leeds, 11-15 May 2009, (done)
• Discrete systems and special functions, 29 June – 3 July 2009. (done)
• Sixth international conference on Computational Methods in Function Theory, Ankara, Turkey, 8-12 June 2009. (done)
• Orthogonal polynomials, special functions and applications (OPSFA10), Leuven, Belgium, 20-25 July, 2009. (well done)
• Workshop on Orthogonal Polynomials, Hankel and Jacobi matrices, Copenhagen, Denmark, August 26-28, 2009. (done)
• Joint Conference of the Belgian and London Mathematical Society, Leuven, Belgium, December 4-5, 2009.

Ph. D. Students

• Ann Sinap: Berekeningsaspecten van orthogonale matrixveeltermen (computational aspects of orthogonal matrix polynomials); March 3, 1995.
• Rudi Maelbrancke: Linear and spatial data structures: new techniques for analysis and optimization (advisors: H. Olivié and W. Van Assche); March 11, 1996.
• Michael Leuschel: Advanced techniques for logic program specialisation (Advisors: D. De Schreye and W. Van Assche); May 27, 1997.
• Lieve Delbeke: Wavelet based estimators for the Hurst parameter of a self-similar process; June 12, 1998.
• Erwin Simons: An efficient multi-domain approach to large-eddy simulation of incompressible turbulent flows in complex geometries (advisors: M. Manna  and W. Van Assche; prepared at von Karman Institute), October 10, 2000.
• Els Coussement: Multiple orthogonal polynomials associated with modified Bessel functions, July 4, 2002
• Jonathan Coussement: Integrable systems of Toda type related to orthogonal functions, February 23, 2005
• Hans Van de Vyver: Runge-Kutta type methods for periodic initial value problems, March 15, 2006
• Christophe Smet: The Hermite-Padé approximation technique for proving irrationality of certain numbers, September 22, 2009
• Lies Boelen: Discrete Painlevé equations and orthogonal polynomials
• François Ndayiragije: Multiple (bi-)orthogonal polynomials

Recent Publications

Books:

· Orthogonal Polynomials and Special Functions: Computation and Applications, Lecture Notes in Mathematics 1883 (F. Marcellán, W. Van Assche)

· Laredo Lectures on Orthogonal Polynomials and Special Functions, Nova Science Publishers (R. Álvarez-Nodarse, F. Marcellán, W. Van Assche)

· Orthogonal Polynomials and Special Functions: Leuven 2002, Lecture Notes in Mathematics 1817 (E. Koelink, W. Van Assche)

· Asymptotics for Orthogonal Polynomials, Lecture Notes in Mathematics 1265 (out of print)

· Difference Equations, Special Functions and Orthogonal Polynomials, proceedings of the international conference, Munich, Germany 25-30 July 2005, World Scientific, 2007 (S. Elaydi, J. Cushing, R. Lasser, A. Ruffing, V. Papageorgiou, W. Van Assche)

· I wrote two chapters in Mourad Ismail’s book: Classical and Quantum Orthogonal Polynomials in One Variable, Encyclopedia of Mathematics and its Applications 98, Cambridge University Press, 2005. These are Chapter 22 (The Riemann-Hilbert Problem) and Chapter 23 (Multiple Orthogonal Polynomials).

Papers:

• Orthogonal polynomials and approximation theory: some open problems (in honor of G. López Lagomasino’s 60^th birthday), Contemporary Mathematics
• Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials (with Lies Boelen), Proc. Amer. Math. Soc.
• Irrationality proof of a q-extension of ζ(2) using little q-Jacobi polynomials (with Christophe Smet), Acta Arithmetica 138, nr. 2 (2009), 165-178
• Mellin transforms for multiple Jacobi-Piñeiro polynomials (with Christophe Smet), J. Approx. Theory
• q-Discrete Painlevé equations for recurrence coefficients of modified q-Freud orthogonal polynomials (with Lies Boelen and Christophe Smet), J. Difference Equations Appl. (to appear)
• Asymptotics of Hermite-Padé rational approximants for two analytic functions with separated pairs of branch points (case of genus 0) (with A.I. Aptekarev and AB.J. Kuijlaars), Internat. Math. Research Papers 2008 (2008), rpm007-128.
• Leonhard Euler and a q-analogue of the logarithm (with Erik Koelink), Proc. Amer. Math. Soc. 137 (2009), 1663-1676.
• Padé and Hermite-Padé approximation and orthogonality, Surveys in Approximation Theory 2 (2006), 61-91.
• Multiple orthogonal polynomials on the unit circle (with Judit Mínguez Ceniceros), Constr. Approx. 28 (2008), 173-197.
• Asymptotic zero distribution for a class of multiple orthogonal polynomials (with E. Coussement and J. Coussement), Trans. Amer. Math. Soc. 360 (2008), 5571-5588.
• Rakhmanov’s theorem for orthogonal matrix polynomials on the unit circle, J. Approx. Theory 146 (2007), 227-242
• Irrationality of z_q(1) and z_q(2) (with K. Postelmans), J. Number Theory 126 (2007), 119-154.
• Chapter 22: The Riemann Hilbert Problem, in “Classical and Quantum Orthogonal Polynomials in One Variable”, M.E.H. Ismail, Cambridge University Press, 2005.
• Chapter 23: Multiple Orthogonal Polynomials, in “Classical and Quantum Orthogonal Polynomials in One Variable”, M.E.H. Ismail, Cambridge University Press, 2005.
• Varying weights for orthogonal polynomials with monotonically varying recurrence coefficients (with A.I. Aptekarev and J.S. Geronimo), J. Approx. Theory 150 (2008), 214-238.
• Differential equations for multiple orthgonal polynomials with respect to classical weights: raising and lowering operators (with J. Coussement), J. Phys. A: Math. Gen. 39 (2006), 3311-3318.
• Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials, Proceedings of the international conference on Difference Equations, Special Functions and Orthogonal Polynomials, World Scientific, 2007, pp. 687-725.
• Type II Hermite-Padé approximation to the exponential function (with A.B.J. Kuijlaars, H. Stahl, F. Wielonsky), J. Comput. Appl. Math. 207 (2007), 227-244.
• WKB and turning point theory for second-order difference equations (with J.S. Geronimo and O. Bruno), Operator Theory: Advances and Applications 154 (2004), 101-138.
• Analytic number theory and approximation, Coimbra Lecture Notes on Orthogonal Polynomials (A.P. Foulquié Moreno et al, eds.), Nova Science Publishers, 2007, pp. 211-243.
• A continuum limit of the relativistic Toda lattice: asymptotic theory of discrete Laurent orthogonal polynomials with varying recurrence coefficients (with J. Coussement), J. Phys. A: Math. Gen. 38 (2005), 3337-3366
• Generalizations of orthogonal polynomials (with A. Bultheel, A. Cuyt, M. Van Barel, B. Verdonk), J. Comput. Appl. Math. 179 (2005), 57-95.
• An extension of the Toda lattice: a direct and inverse spectral transform connected with orthogonal rational functions, (with J. Coussement), Inverse Problems 20 (2004), 297-318.
• Multiple little q-Jacobi polynomials (with K. Postelmans), J. Comput. Appl. Math. 178 (2005), 361-375.
• Gauss quadrature for multiple orthogonal polynomials (with J. Coussement), J. Comput. Appl. Math. 178 (2005), 131-145.
• Quadratic Hermite-Padé approximation to the exponential function: a Riemann-Hilbert approach (with A.B.J. Kuijlaars and F. Wielonsky), Constr. Approx. 21 (2005), 351-412.
• Asymptotique des approximants de Hermite-Padé quadratiques de la fonction exponentielle et problèmes de Riemann-Hilbert (with A. Kuijlaars, H. Stahl and F. Wielonsky), C. R. Acad. Sci. Paris, Ser. I 336 (2003), 893-896.
• Multiple Wilson and Jacobi-Piñeiro polynomials (with B. Beckermann and J. Coussement), J. Approx. Theory 132 (205), 155-181.
• Asymptotics of orthogonal polynomials by three term recurrence relations (with D.W. Lee)
• Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight (with A. I. Aptekarev), J. Approx. Theory 129 (2004), 129-166.
• Analysis of non-linear recurrence relations for the recurrence coefficients of generalized Charlier polynomials (with M. Foupouagnigni), J. Nonlinear Math. Phys. 10 Supplement 2 (2003), 231-237.
• Difference equations for multiple Charlier and Meixner polynomials in New Progress in Difference Equations (S. Elaydi et al., eds.), Taylor & Francis, London, 2003, pp. 547-555.
• Szegö quadrature and frequency analysis (with L. Daruis, O. Njåstad), ETNA 19 (2005), 48-57.
• Para-orthogonal polynomials in frequency analysis (with L. Daruis, O. Njåstad), Rocky Mountain J. Math. 33 No. 2 (2003), 629-645.
• Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials (with J. Coussement and A.B.J. Kuijlaars), Inverse Problems 18 (2002), 923-942.
• Blumenthal's theorem for Laurent orthogonal polynomials (with A. Sri Ranga), J. Approx. Theory 117 (2002), 255-278.
• The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1] (with A.B.J. Kuijlaars, K.T-R McLaughlin, and M. Vanlessen), Adv. Math. 188 (2004), 337-398.
• Strong asymptotics for relativistic Hermite polynomials (with W. Gawronski), Rocky Mountain J. Math. 33 No. 2 (2003), 489-524.
• Some discrete multiple orthogonal polynomials (with J. Arvesú and J. Coussement), J. Comput. Appl. Math.153 (2003), 19-45.
• Asymptotics of multiple orthogonal polynomials associated with the modified Bessel functions of the first kind (with E. Coussement), J. Comput. Appl. Math. 153 (2003), 141-149.
• Multiple orthogonal polynomials associated with the modified Bessel functions of the first kind (with E. Coussement), Construct. Approx. 19 (2003), 237-263.
• Multiple orthogonal polynomials for classical weights (with A.I. Aptekarev and A. Branquinho), Trans. Amer. Math. Soc. 355 (2003), 3887-3914.
• Riemann-Hilbert problems for multiple orthogonal polynomials (with J.S. Geronimo and A.B.J. Kuijlaars), in  Special Functions 2000: Current Perspectives and Future Directions (J. Bustoz et al., eds.), NATO Science Series II. Mathematics, Physics and Chemistry 30, Kluwer, Dordrecht, 2001, pp. 23-59.
• Some classical multiple orthogonal polynomials (with E. Coussement), J. Comput. Appl. Math. 127 (2001), 317-347
• Little q-Legendre polynomials and irrationality of certain Lambert series, The Ramanujan Journal 5 (2001), 295-310.
• Entropic integrals of hypersperical harmonics and spatial entropy of D-dimensional central potentials, (with R. J. Yáñez, R. González-Férez and J. S. Dehesa), J. Math. Phys. 40  (1999), 5675-5686.
• Functionals of Gegenbauer polynomials and D-dimensional hydrogenic momentum expectation values, (with R. J. Yáñez, R. González-Férez and J. S. Dehesa), J. Math. Phys. 41 (2000), 6600-6613.
• Information entropy of Gegenbauer polynomials, (with V. S. Buyarov, P. López-Artés, A. Martínez-Finkelshtein), J. Phys. A, Math. Gen. 33 (2000), 6549-6560.
• Nonsymmetric linear difference equations for multiple orthogonal polynomials, proceedings of SIDEIII (Symmetry and Integrability of Difference Equations), CRM Proceedings and Lecture Notes 25, Amer. Math. Soc., 2000, pp. 391-405.
• Lamé differential equations and electrostatics, (with Dimitar K. Dimitrov), Proc. Amer. Math. Soc. 128 (2000), 3621-3628 (see also the erratum)
• Zero distribution of orthogonal polynomials with asymptotically periodic varying recurrence coefficients, proceedings of Self-Similar Systems, Dubna, Russia, 1998, pp. 392-402.
• Multiple orthogonal polynomials, irrationality and transcendence, in Continued Fractions: from analytic number theory to constructive approximation, Contemporary Mathematics 236, Amer. Math. Soc., 1999, pp. 325-342
• Spectral representation of certain finite birth and death processes, (with P. R. Parthasarathy and R. B. Lenin), The Math. Scientist 24 (1999), 105-112
• Multiple orthogonal polynomials associated with Macdonald functions, (with S.B. Yakubovich), Integral Transforms and Special Functions 9 (2000), 229-244
• Asymptotics for polynomials satisfying a certain twin limit periodic recurrence relation, (with E.X.L. de Andrade and A. Sri Ranga), Methods and Applications of Analysis 6 (1999), 535-548
• The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients (with A. B .J. Kuijlaars), J. Approx. Theory 99 (1999), 167-197
• A birth and death process related to the Rogers-Ramanujan continued fraction (with P. R. Parthasarathy, R. B. Lenin and W. Schoutens), J. Math. Anal. Appl. 224 (1998), 297-315
• Asymptotic behavior of the continued fraction coefficients of a class of Stieltjes transforms including the Binet function (with W. B. Jones), Orthogonal Functions, Moment Theory and Continued Fractions (W.B. Jones, A. Sri Ranga, eds.), Marcel Dekker, 1998, pp. 257-274
• Extremal polynomials on discrete sets (with A. B. J. Kuijlaars), Proc. London Math. Soc. (3) 79 (1999), 191-221
• Approximation theory and analytic number theory, Special Functions and Differential Equations (K. Srinivasa Rao et al., eds.), Allied Publishers, New Delhi, 1998, pp. 336-355.
• Perturbation of orthogonal polynomials on an arc of the unit circle, II, (with L. Golinskii, P. Nevai and F. Pinter), J. Approx. Theory 96 (1999), 1-33.
• A contact problem in elasticity related to weighted polynomials on the real line (with A.B.J. Kuijlaars), Rend. Circ. Mat. Palermo, serie II, 52 (supplemento), volume II (1998), 575-587
• A problem of Totik on fast decreasing polynomials(with A.B.J. Kuijlaars), Constr. Approx. 14 (1998), 97-112
• A wavelet based estimator for the parameter of self-similarity of fractional Brownian motion (with Lieve Delbeke)
• A wavelet based estimator for the parameter of self-similarity of fractional Brownian motion (with Lieve Delbeke), Aportaciones Matematicas  (a short version of the previous paper)
• Information entropy of classical orthogonal polynomials and their application to the harmonic oscillator and Coulomb potentials(with J.S. Dehesa and R.J. Yanez), Methods Appl. Anal. 4 (1997), 91-110
• Compact Jacobi matrices: from Stieltjes to Krein and M(a,b), Ann. Fac. Sci. Toulouse, numéro special Stieltjes (1996), 195-215
• Perturbation of orthogonal polynomials on an arc of the unit circle (with L. Golinskii and P. Nevai), J. Approx. Theory 83 (1995), 392-422
• Upward extension of the Jacobi matrix for orthogonal polynomials (with A. Ronveaux), J. Approx. Theory 86 (1996), 335-357
• Orthogonal polynomials in the complex plane and on the real line, Special Functions, q-Series and Related Topics (M.E.H. Ismail et al., eds.), Fields Institute Communications 14 (1997), 211-245
• The impact of Stieltjes' work on continued fractions and orthogonal polynomials: additional remarks (with G. Valent), J. Comput. Appl. Math. 65 (1995), 419-447
• Orthogonal matrix polynomials and applications (with A. Sinap), J. Comput. Appl. Math. 66 (1996), 27-52
• Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator (with J.S. Dehesa and R.J. Yanez) J. Math. Phys. 36 (1995), 4106-4118
• Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function (with H.T. Koelink), Constr. Approx. 11 (1995), 477-512

Interesting Mathematical Links

Organizations

• SIAM Activity Group: Orthogonal Polynomials and Special Functions
• OPSFtalk: a discussion forum in orthogonal polynomials and special functions
• SIAM
• American Mathematical Society
• European Mathematical Information Service
• Belgian Mathematical Society
• Wiskundig Genootschap (Nederland)
• Surveys in Approximation Theory
• Zentralblatt fur Mathematik and Searching in Zentralblatt
• Mathematics Subject Classification 2000
• Mathematisches Forschungsinstitut Oberwolfach
• Approximation Theory Net
• Classical Analysis (CA) section of the xxx math archives.
• Center of Hypergeometric Systems, Kobe, Japan.
• Training and Mobility of Researchers (European Commission: Science Research Development)
• Maple
• Wolfram (Mathematica)
• Centre for Experimental and Constructive Mathematics
• Stieltjes Institute

Journals

• Journal of Approximation Theory
• JAT Editorial WWW
• Constructive Approximation
• Surveys in Approximation Theory
• ETNA Electronic Transactions on Numerical Analysis
• SIAM journals
• Electronic Research Announcements of the AMS
• Elsevier journals (science-direct)
• Springer journals

Publishers

• Springer-Verlag
• Cambridge University Press
• Oxford University Press
• Elsevier
• World Scientific
• Institute of Physics
• Addison-Wesley
• Birkhauser

Personal Homepages

• Paul Nevai
• Peter Borwein
• Doron Zeilberger
• Alphonse Magnus
• Ed Saff
• Erik Koelink
• Tom Koornwinder
• Wolfram Koepf
• Andrei Martínez Finkelshtein
• Jeff Geronimo

Software

• Personal TeX
• Available Mathematical Software
• TeX archives
• Maple
• Wolfram (Mathematica)

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This file is maintained by walter at wis.kuleuven.be