Summer School
on Orthogonal Polynomials and Special Functions:
Approximation and Iteration

Departamento de Matemática,
Universidade de Coimbra, Portugal
14
26 July
2003

Table of contents 

Goal of the Course and Additional
Information 

The SIAM Activity Group (SIAG) on Orthogonal Polynomials and Special
Functions organizes a series of summer schools. The first of this series was the
school in Laredo,
Spain, in 2000, the second in
Inzell, Germany, in the
Alps southeast of Munich from September 1723, 2001, and the third in
Leuven, Belgium,
in 2002.

It is planed to continue in 2004 in Carlos III University, Spain. 
The goal of the Summer School is to give four introductory
10 hours courses
and 4 hours
minicourses in advanced
research topics on orthogonal polynomials, approximation and iteration theory.
The titles can be found below. Some free discussions
and some informal seminars will also be available. The expected audience are
graduate and recent postgraduate students as well as young active researchers. 
Also there will be special
sessions where the participants will have the opportunity to give some short
research seminars as well as a panel discussion. Because of the reduced numbers
of these seminars we kindly ask to such participants who want to present their
own results to send us as soon as possible the abstract. Priority will be given
to those talks close related to the main subjects of the school. 
The contributed talks should not exceed the length of 20 minutes. Please
consider that we have two overhead and computer projectors in the lecture
room, and a blackboard. 

Orthogonal Polynomials 
Approximation Theory 
Iteration theory 
Matrix moment problems 
Birth and death processes 
Integral Transforms 
Number Theory 

This year
Coimbra is the portuguese capital of culture. 

Every day there will be a visit to the old part of
Coimbra
University. 
The wednesday afternoon are free of lectures, and
we plan
a visit to the Roman town of Conimbriga (12 Km far from Coimbra) and the old
part of our University, and by night we have a
conference dinner. 


Coimbra can easily be reached by
car (close to the highway A1, LisbonPorto)
and train (200 km from Lisbon
International Aiport and 100 km from Porto International Airport).

The railway station you have to take, if you come by
plane is Campanhã in Porto and Gare do Oriente in Lisbon.
See train schedules at the web page
CPschedules
and prices at
CPprices. 
The university has experience in organizing conferences. Furthermore the Summer Course
is planned during the academic holiday so that there is no interference with
regularly scheduled classes or seminars. 

The participants stay in Hotels IBIS and Almedina,
and Residenciais Alentejana, Antunes and Botânico. 
Hotel 
Single 
Double 
Triple 
Address 
Phone 
Residencial Alentejana 
33€ 
43€ 

R. Dr. Henrique Seco, 1 
+351 239825924 
Residencial Antunes 
34,5€ 
43,10€ 
54€ 
R. Castro Matoso, 8 
+351 239854720 
Residencial Botânico 
34,5€ 
39€ 

R. Bairro de S. José, 15 
+351 239714824 
Hotel IBIS 
48,74€ 


R. Emídio Navarro 
+351 239852130 
Hotel Almedina 
42,35€ 
50,16€ 

R. Fernão de Magalhães, 199 
+351 239855500 


The local organizing committee for this summer school consists of: 
Amílcar Branquinho,
Departamento de Matemática da Universidade de Coimbra, Coimbra, Portugal. 
Ana Foulquié, Departamento de
Matemática da Universidade de Aveiro, Aveiro, Portugal. 
The scientific committee, acting for the whole series of summer schools
20012004 consists of: 
Amílcar Branquinho, Universidade de Coimbra, Portugal 
Erik Koelink, Technische Universiteit Delft, the Netherlands 
Rupert Lasser, GSFForschungszentrum für Umwelt und Gesundheit and
Technische Universität München, Germany 
Francisco Marcellán, Universidad Carlos III de Madrid, Spain 
Walter Van Assche, Katholieke Universiteit Leuven, Belgium 

C. Berg (Kobenhavns Universitet, Kobenhavn, Denmark):
Matrix moment problems. 
J. Bustoz* (Arizona State University, USA): Classical summability theory and qseries. 
G. López Lagomasino (Universidad Carlos III de Madrid,
Madrid, Spain): Constructive theory of
approximation. 
F. Marcellán (Universidad Carlos III de
Madrid, Spain): Orthogonal polynomials and Sobolev inner products. 
F. Peherstorfer (Johannes Kepler Universität Linz, Linz,
Austria): Iteration theory and orthogonal
polynomials. 
W. Van Assche (Katholieke Universiteit Leuven,
Belgium): Analytic Number Theory. 
E. Van Doorn (Universiteit Twente, Enschede, the
Netherlands): Birth and death processes and
orthogonal polynomials. 
S. Yakubovich (Universidade do Porto,
Portugal): Integral Transforms of Hypergeometric Functions. 
*Due to health problems Professor
Joaquin Bustoz cannot present the course "Classical summability theory and
qseries". The organizing committee wishes him a quick recover and hopes that in
one of the next meetings he will be again among the participants. 
Work Program:
Room Pedro Nunes in the Department of Mathematics, School
of Sciences and Technology, University of Coimbra 
First Week 

Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Opening session 
9h9h25m 




Christian Berg 
9h30m11h30m 
9h11h 
9h11h 
9h11h 
9h11h 
coffee
break 
11h30m12h
16h16h20m 
11h11h30m
16h16h20m 
11h11h30m 
11h11h30m
16h16h20m 
11h11h30m
16h16h20m 
Erik Van Doorn 
12h13h
15h16h 
11h30m13h30m 
11h30m13h30m 
11h30m13h30m 
11h30m13h30m 
lunch 
13h15h 
13h30m15h 
13h30m14h30m 
13h30m15h 
13h30m15h 
Semyon
Yakubovich 

15h16h
16h20m17h20m 


15h16h
16h20m17h20m 
Short Communication 
16h20m18h: 5,6 
17h20m18h:
2 

15h16h:
10,11
16h20m18h: 4,7 
17h20m18h:
12 
cultural program 


14h30m18h 



Room José
Anastácio da Cunha 
Second Week 

Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Guillermo López
Lagomasino 
9h11h 
9h11h 
9h11h 
9h11h 
9h11h 
coffee break 
11h11h30m
16h16h20m 
11h11h30m
16h16h20m 
11h11h30m 
11h11h30m
16h16h20m 
11h11h30m
16h16h20m 
Franz Peherstorfer 
11h30m13h30m 
11h30m13h30m 
11h30m13h30m 
11h30m13h30m 
11h30m13h30m 
lunch 
13h30m15h 
13h30m15h 
13h30m14h30m 
13h30m15h 
13h30m15h 
Walter Van Assche 
15h16h 
15h16h 

15h16h 
15h16h 
Francisco Marcellán 
16h20m17h20m 
16h20m17h20m 

16h20m17h20m 
16h20m17h20m 
Short Communication 
17h20m18h: 8 
17h20m18h: 3 

17h20m18h: 9 
17h20m18h: 1 
cultural program 


14h30m18h 





Title: Matrix Moment Problems 
Abstract:

Complex measures and matrix.valued measures. 
Compact sets of positive matrixvalued
measures. 
Krein's Theorem characterizing matrix
moment sequences. 
Matrix inner products and orthonormal
matrix polynomials. 
Indeterminate matrix moment problems and
NJacobi matrices. 

Title:
Classical summability theory and qseries 
Abstract:
The classical theory of summability was an important
area of research from about 1900 to about 1960. Although there
is still very good work being done in the subject, there has been
a substantial reduction in interest. In these lectures we will
give a brief overview of classical results including Hausdorff
summability and Gronwall summability. We will discuss applications
to trigonometric Fourier series and to univalent functions. Next
we will discuss recent developments in ''qFourier series'' on
both qquadratic and qlinear grids. Then we will establish
connections between qseries and classical summability methods
that produce new methods of summability. We will give some
applications of these qsummability methods and finish with some
open questions. 

Title:
Constructive Theory of Approximation 
Abstract:

Padé approximation. Definition and basic properties. 
Hadamard´s Theorem on the radii of mmeromorphy of an analytic function. 
Montessus de Ballore's Theorem on the location and order of poles. 
Inverse problems for row sequences of Padé approximants. 
Possible extensions of the previous results to multipoint Padé
approximants, orthogonal expansions and expansions in terms of Faber
polynomials. 
Theorems of Markov and Stieltjes on the convergence of diagonal Padé
approximants. 
Inverse problems for diagonal sequences of Padé approximants. Gonchar´s
Theorem. 
Extension of the Theorems of Markov. Stieltjes and Gonchar to other types
of expansions. 

Title:
Orthogonal polynomials and Sobolev inner products 
Abstract: An introduction to the recent trends
and main results in the theory of orthogonal polynomials with respect to Sobolev
inner products is the aim of this set of lectures. We will focus our attention
in some open problems.
Lecture notes with selfcontained exercises will
be provided to the participants in the summer school. 
Standard orthogonality versus orthogonality with
respect to Sobolev inner products.

Multiplication operator in Sobolev spaces. Some
applications to the location of zeros of orthogonal polynomials.

Asymptotic properties of Sobolev orthogonal
polynomials.

Differential operators in Sobolev spaces. Regular
and singular second order boundary value problems.

Fourier expansions and Sobolev orthogonal
polynomials. 

Title:
Lectures on Iteration of functions and orthogonal polynomials 
Abstract: 
Part I: Iteration of one dimensional maps. 

Periodic points and stable sets: Theorem of
LiYorke ( = "Period 3 implies chaos''), Theorem of Sharkovskii (existence
and order of periodic points) and Theorem of Singer (Schwarz's derivative and
the maximal number of attracting cycles).

Bifurcation: Important types of
bifurcations as pitchfork, saddle node and period doubling bifurcations
Example: family of logistic functions.

Chaotic maps:

(a)
Definition, sensitive dependence on initial conditions, Lyapunov exponents; 
(b) Symbolic
dynamics and conjugacy; 
(c)
Investigation of the chaotic behaviour of the logistic function, consequences
for population models. Unimodal
functions and the Feigenbaum constant; 
(d)
Invariant measuresPerron Frobenius
Operator, Orthogonal polynomials. 
Part II: Julia and Mandelbrot set 
 Iteration of polynomials
and of rational functions in the complex plane:

(a) Julia set 
periodic points  family of normal functions; 
(b) How to get the
Julia set; 
(c) Mandelbrot set
and the geometry of the Julia set of the quadratic family; 
(d) Orthogonal and extremal polynomials on
sets invariant under a polynomial map, in particular on Julia sets. 

(a) Nonlinear maps and Jacobian matrix 
(b) Stable and
unstable manifolds 
(c) Chaotic maps: Hénon map, horseshoe  map 
(d) Connection between differential equations
and discrete dynamical systems: the Poincaré map. 

Title:
Analytic Number Theory 
Abstract: In this course we will cover some
aspects of analytic number theory, in particular rational approximation of
irrational numbers, irrationality proofs and transcendence proofs. Quite often
the construction of rational approximants to real numbers is by means of
continued fractions, Padé approximation or HermitePadé approximation. The
following topics will be covered: 
Continued fractions in number theory. 
Algebraic and transcendental numbers. 
Irrationality proofs; irrationality of e
and .

Padé approximation.

Irrationality of
and qextensions
of the harmonic series.

HermitePadé approximation.

Irrationality of ,
and .

Transcendence proofs; transcendence of e. 
Irrationality measures; Roth's theorem.


Title:
Orthogonal Polynomials and BirthDeath Process 
Abstract:
The course will be an introduction to the theory of birthdeath
processes with emphasis on the role played by orthogonal polynomials in the
analysis of these processes. The general theme of the course will be the
phenomenon that the problem of extracting certain information about a
birthdeath process from the parameters defining the process can often be
translated into a problem extracting information about a set of orthogonal
polynomials and the associated measure from the parameters in the recurrence
relation satisfied by these polynomials. 
Topics addressed in the course include: birthdeath polynomials, the KarlinMcGregor (or spectral) representation, recurrence and transience, ratio limits,
exponential ergodicity, speed of convergence to stationarity, quasistationarity,
limiting conditional distributions, first entrance and return times, random
walks (discretetime birthdeath processes), birthdeath fluid models. 
Many examples will be given to illustrate the concepts and results.Abstract: The course will be an introduction to the theory of birthdeath
processes with emphasis on the role played by orthogonal polynomials in the
analysis of these processes. The general theme of the course will be the
phenomenon that the problem of extracting certain information about a
birthdeath process from the parameters defining the process can often be
translated into a problem extracting information about a set of orthogonal
polynomials and the associated measure from the parameters in the recurrence
relation satisfied by these polynomials. 
Topics addressed in the course include: birthdeath polynomials, the KarlinMcGregor (or spectral) representation, recurrence and transience, ratio limits,
exponential ergodicity, speed of convergence to stationarity, quasistationarity,
limiting conditional distributions, first entrance and return times, random
walks (discretetime birthdeath processes), birthdeath fluid models. 
Many examples will be given to illustrate the concepts and results. 

Title:
Integral Transforms of Hypergeometric Functions 
Abstract: The Mellin transform and the notion of
hypergeometric functions; Gamma function and the MellinBarnes integrals;
Bessel functions and classical transforms; Composition method of integral
transformations and general transform;
Nonconvolution integral transformations; Introduction to the class of the
KontorovichLebedev type integral transformations. 
References: 

Akhiezer, N.I. "Lectures on integral transforms". AMS. 1988. Vol. 70.

Marichev, O. "Handbook of integral transforms of higher transcendental
functions, theory and algorithmic tables". Ellis Horwood. 1982.

Yakubovich, S. "Index Transforms", World Scientific, 1996.

Yakubovich, S. and Luchko, Yu. "Hypergeometric approach to integral
transforms and convolutions", Kluwer. 1994.



Title. Generating Functions for Several Variables Classical Orthogonal
Polynomials. 
Abstract.Classical
orthogonal polynomials in one variable are the unique set of orthogonal
polynomials in one variable which can be defined by a Rodrigues type formula.
Using Lagrange formula we can get a generating function for polynomials. In
this work, we use an extension of Lagrange formula to polynomial sequences of
two variables, to obtain a generating function of the following types of
orthogonal polynomial sequences: Hermite×Hermit classical families, circle
polynomials and triangular polynomials. 

Title.
A moment problem and a family of integral evaluations. 
Abstract. The
AskeyWilson integral tells us how to integrate the product of four generating
functions for the continuous qHermite polynomials times their weight
function. In a similar way one can take the product of four generating
functions for the q^{1}Hermite polynomials as a starting point. But since
the q^{1}Hermite moment problem is indeterminate, infinitely many
integrals (with the same value) are coming up, one for each solution to the
moment problem. In the talk a new family of weight functions for the q^{1}Hermite polynomials will be presented and the corresponding integrals
will be given as well.
A function f(x) with x= sinh y can be viewed as a function of
e^{y} and we
shall use the notation $\breve{f}(e^y):=f(x)$. The divided difference operator
$\mathcal{D}_q$ defined by \[
\mathcal{D}_qf(x)=\frac{\breve{f}(q^{1/2}e^y)\breve{f}(q^{1/2}e^y)}
{(q^{1/2}q^{1/2})\cosh y}, \quad x=\sinh y \]
is a lowering operator for the q^{1}Hermite polynomials. In fact,
$ \mathcal{D}_q$ is a bounded operator on the weighted L^{2}spaces in which the
q^{1}Hermite polynomials are dense. The right inverse of $\mathcal{D}_q$
can be identified as an integral operator and an explicit expression for the
kernel will be derived. 
Symmetric coherent pairs were introduced by A. Iserles et al. in 1991, and H.
G. Meijer gave a description of them in 1997. Moreover, if (\ref{1}) holds,
then we get \begin{equation}\label{2} T_n + s_{n} T_{n2} =
\frac{P'_{n+1}}{n+1} + u_{n} \frac{P'_{n1}}{n1}. \end{equation} The aim of
our contribution is to describe the moment functional $v$ assuming that $w$ is
classical and that the corresponding sequences of monic orthogonal polynomials
satisfy (\ref{2}). Then, we obtain a result announced by Sri Ranga and others
in 2001. 

Title.
Number Theory, qcalculus. The Zeta and qZeta functions. 
Abstract. We give a simple introduction of Number theory and some
applications related with cyclothomic polynomials, qcalculus and the Zeta
function and its natural q extenssions as well as some identities of these
functions. Besides, we give some applications related with this functions. 

Title.
On an extension of symmetric coherent pairs of orthogonal polynomials. 
Abstract. Given two positive symmetric moment functionals $w,v$ and $\{
P_n \}, \{ T_n \}$ the corresponding sequences of monic orthogonal polynomials
for $w,v$ respectively, if they are related by \[ T_n=\frac{P'_{n+1}}{n+1} +
u_{n} \frac{P'_{n1}}{n1}, \] then the pair $(w,v)$ is said to be a symmetric
coherent pair. In this case we can prove that \begin{equation}\label{1} P_n +
u_{n} P_{n2} = Q_n^\lambda + d_{n} Q_{n2}^\lambda, \end{equation} where
$Q_n^\lambda$ are monic orthogonal polynomial with respect to the Sobolev
bilinear form $\varphi (p,q)= w(p\,q) + \lambda v(p'\,q')$. 

Title.
ParaOrthogonal
Polynomials and Quadrature Formulas on [0,1] . 
Abstract.
We establish a relation between quadrature
formulas on the interval $[ 
1, 1]$,
that approximate integrals of the form $J_\mu
(F) = \int_{1}{1} F(x) \mu (x)dx$,
and Szegö
quadrature formulas on the unit circle that approximate integrals of the form
$I (f) =\int_{1}{1} f (e^{i \theta}) w
(\theta) d \theta$.
The
functions $\mu (x)$ and $w (\theta)$ are assumed to be weight functions on $[

1, 1]$
and $[\pi,\pi];
respectively, and related by $w (\theta) = \mu (cos
\theta)\sin \theta$. It
is well known that the nodes of Szegö
formulas are the zeros of the so called paraorthogonal polynomials $B_n (z,\tau)
= \Phi_n (z) + \tau \Phi_n^* (z)$, $\tau= 1$, $\Phi_n (z)$ and $\Phi_n^*$
being the orthogonal and reciprocal polynomials, respectively, with respect to
the weight function $w(\theta)$.
Furthermore, for $\tau = \pm 1$ we have recently
obtained Gausstype quadrature formulas on $[ 
1, 1]$.
In this work, making use of the paraorthogonal polynomials with $\tau \not= \pm
1$, a oneparameter family of interpolatory quadrature formulas with positive
coefficients for $J_\mu (F)$ is obtained. Some illustrative numerical examples
are also included. 

Title.
Orthogonal
Polynomials in FiniteDimensional Spaces. 
Abstract. Denote by ${\cal
P}(a)$ the algebra of all polynomials (with complex coefficients) modulo the
monic polynomial $a(\zeta)$ of exact degree $L$. Let further $M$ be a
Hermitian positive definite $L$by$L$ matrix. We consider the inner product
on ${\cal P}(a)$ which is defined by $(\zeta^j,\zeta^k)=M(k,j)$ ($0 \le j,k
\le L1$) and investigate certain properties of the corresponding orthogonal
and kernel polynomials. Special emphasis is put on the questions under which
conditions these polynomials satisfy short recurrence relations. 

Title.
Electrostatic interpretation of zeros of semiclassical orthogonal polynomials. 
Abstract.
Polynomials orthogonal with respect to a perturbation of certain classical
weight functions by the addition of mass points at the end points of the
interval $\Omega\subset\mathbb{R}$ are considered. These polynomials satisfy a
second order linear differential equation with varying polynomial coefficients
depending on $\lambda\in\mathbb{R}^+$. Indeed, such a differential equation
leads to an electrostatic problem for $n$ positive charges in the interval
with a varying external field and fixed charges at the end points. We show
that for $n$ large enough the zeros of the orthogonal polynomials minimize the
electrostatic energy for $n$ movable charges in the corresponding
electrostatic equilibrium problem. 

Title. Asymptotic error estimate for Krylov's
subspaces methods. 
Abstract. Using the logarithmic potential theory, we
study asymptotic error of Krylov subspace methods. We work at the moment on a
convectiondiffusion equation and especially on the linear system arising from
a finite difference discretization, solved with GMRES. First, we study the
eigenvalues asymptotic distribution of the preconditioned linear system.
Secondly, we use results about constrained energy problems in logarithmic
potential theory. 

Title.
Convergence classes for analytic functions represented by AbelGoncharov
series. 
Abstract.The aim of this short communication is to present a study about
representation of analytic functions by AbelGoncharov series. To do this, we
begin by introducing Goncharov polynomials and its main properties. Goncharov
interpolation problem is refered and we show a theorem by Polya which gives a
sufficient condition of convergence to the interpolation problem in the
periodic case. Then we show some results about uniqueness and convergence
classes of analytic functions which are represented as series whose
coefficients are functionals. Some examples are given: Newton series, Abel
series and AbelGoncharov series. 

Title.
Entropic
Integrals of Special Functions: Airy Function. 
Abstract. The
asymptotics of special functions other than classical orthogonal polynomials
will be discussed in the configuration space, as well as in the
"Fouriertransformed" space. Emphasis will be put in the Airy function. This
kind of special function naturally describes the quantummechanical wave
function of the dynamical states of a charged particle moving in a external
electric field of homogeneous character. 

Title.
Information Entropy of Gegenbauer Polynomials and Gaussian. 
Abstract.
During the last decade there has been an intense activity in the study of the
information entropies associated to the classical orthogonal polynomials,
motivated by their relevance to quantum physics and their close relationship
to other interesting mathematical objects, such as the $L^p$norms or the
logarithmic potentials of the polynomials. In a recent paper (V. S. Buyarov et
al. 2000) an efficient method was provided for evaluating in closed form the
logarithmic potential and the entropy of Gegenbauer polynomials with integer
parameter. The application of this method to the polynomial $C_n^{(l)} (x)$ ($l
\in \mathbb{N}$) requires the computation by means of recurrence relations of
two auxiliary polynomials, $P(x)$ and $H(x)$, of degrees $2l2$ and $2l4$,
respectively. Here it is shown that $P(x)$ is related to the Christoffel
coefficients of the Gaussian quadrature formula for the Gegenbauer weight $w_l(x)
= (1x^2)^{l1/2}$, and this fact is used to obtain the explicit expression of
$P(x)$. From this result, an explicit formula is also given for the polynomial
$S(x) = \lim_{n \rightarrow \infty} P \big( 1x/(2n^2) \big)$, which plays a
key role in the study of the asymptotic ($n \to \infty$ with $l$ fixed)
behaviour of the entropy. 

Title.
Monotonicity
properties and inequalities of the zeros of qassociated polynomials. 
Abstract. Using a functional analytic method, based on the three terms
recurrence relations that the qassociated polynomials satisfy , we present
some monotonicity results and inequalities of the zeros of the orthogonal
polynomials under consideration. The obtained results unify, generalize and
improve previously known results. 

All registrations for the Summer School on Orthogonal Polynomials and
Special Functions must be submitted via Web using the electronic
registration form, or by fax, mail or email to the Congress Secretariat

Secretária do Euro Summer Course on OPSF 2003, Departamento de
Matemática FCT, Universidade de Coimbra, Apartado 3008, 3000 Coimbra,
Portugal.

Fax Number: +351 239832568.
using pdf
registration form.


Abrantes,
Mário António Grande. address. Instituto Politécnico de Bragança,
Escola Superior de Tecnologia e de Gestão de Bragança, Ap. 134, 5301857 Bragança,
Portugal. 
Alvarez
Rocha,
Ignacio. address. Universidad Politécnica de Madrid, Dpto. Matematica Aplicada. E.U.I.T. Telecomunicacion. Ctra. de Valencia Km 7. 28031 Madrid,
Spain. 
Azevedo,
José. address. ISCAPIPP, Travessa das Ribeirinhas, 95, 4430511
Vila Nova de Gaia, Portugal. 
Beckermann,
Bernahardt. address. Universite des Sciences et Technologies de Lille 1,
UFR de Mathematiques, Bat. M3, USTL, 59655 Villeneuve d'Ascq cedex,
France. 
Berg, Christean. Address.
Kobenhavns Universitet, Kobenhavn, Denmark. 
Bouras,
Belgacem. address. Faculté de Science de Sfax, I.S.S.A.T Gabes route de Mednine,
Tunisia. 
Cantero Medina,
María José. address. Universidad de Zaragoza, Departamneto de Análisis Económico,
Facultad de CCEE y EE. Gran Vía, 2. 50005 Zaragoza, Spain. 
Christiansen,
Jacob Stordal. address. University of Copenhagen, Universitetsparken 5, 2100 Copenhagen,
Denmark. 
CostasSantos,
Roberto Santiago. address. Universidad Carlos III, Ave. Universidad, 30,
28911 LeganésMadrid, Spain. 
Cotrim,
Luís. address. Escola Superior de Tecnologia e Gestão do
I.P.L., Quinta do Seixo lote 1  4 Dto 2410 Leiria, Portugal. 
Coussement,
Jonathan. address. Katholieke Universiteit Leuven, Celestijnenlaan 200 B 3001 Leuven,
Belgium. 
Daruis,
Leyla. address. Universidad de la Laguna, Departamento
de Análisis Matemático, Av. Francisco Sánchez, S/N, 38271 La Laguna.
Tenerife, Islas Canarias, Spain. 
Daems,
Evi. address. Katholieke Universiteit Leuven, Celestijnenlaan 200 B 3001 Leuven,
Belgium. 
Delgado Amaro,
Antonia María. address. Universidad Carlos III, Ave. Universidad, 30,
28911 LeganésMadrid, Spain. 
Eiermann,
Michael. address. TU Bergakademie Freiberg, Agricolastr. 1, D09596 Freiberg,
Germany. 
Freitas,
José Orlando G. address.
Universidade da Madeira, Departamento de Matemática e Engenharias, Campus Universitário da Penteada
9000390 Funchal, Portugal. 
Garrido Berenguel,
Ángeles. address. Universidad Carlos III, Ave. Universidad, 30,
28911 LeganésMadrid, Spain. 
Ghrissi,
Abdallah. address. Faculté de Science de Sfax, I.S.S.A.T Gabes route de Mednine,
Tunisia. 
Helsen,
Steff. address. Katholieke Universiteit Leuven, Celestijnenlaan 200 B 3001 Leuven,
Belgium. 
Hernandez Benitez,
Javier. address. Universidad Carlos III, Ave. Universidad, 30,
28911 LeganésMadrid, Spain. 
Inglart,
Mélissa. address. Universite des Sciences et Technologies de Lille 1,
UFR de Mathematiques, Bat. M3, USTL, 59655 Villeneuve d'Ascq cedex,
France. 
Krystek,
Anna. address. Institute of Mathematics, Wroclaw University,
pl. Grunwaldzki 2/4, Poland. 
López Lagomasino, Guillermo.
address. Universidad Carlos III de Madrid,
Madrid, Spain. 
López Garcia,
Abey. address. Universidad Complutense de Madrid, C/Horizon, 3I, 6A,
Spain. 
Loureiro,
Ana. address. Instituto Superior de Engenharia de Coimbra,
Rua Pedro Nunes, 3030199 Coimbra, Portugal. 
Marcellán, Francisco. address. Universidad Carlos III de Madrid,
Madrid, Spain. 
Marques, Jorge. address. Universidade de Coimbra,
Faculdade de Economia, Av. Dias da Silva, 165, 3030 Coimbra, Portugal. 
Matos,
Ana Cristina. address. Universite des Sciences et Technologies de Lille 1,
UFR de Mathematiques, Bat. M3, USTL, 59655 Villeneuve d'Ascq cedex,
France. 
Mendes,
Ana Isabel. address. Escola Superior de Tecnologia e Gestão do
I.P.L., Quinta do Seixo lote 1  4 Dto 2410 Leiria, Portugal. 
Mlotkowski,
Wojtek. address. Institute of Mathematics, Wroclaw University,
pl. Grunwaldzki 2/4, Poland. 
Nascimento,
Alexandra. address. Escola Superior de Tecnologia e Gestão do
I.P.L., Quinta do Seixo lote 1  4 Dto 2410 Leiria, Portugal. 
Nascimento Sequeira,
Alcino. address. Instituto Superior de Engenharia de Coimbra Rua Pedro Nunes  Quinta da Nora 3030199
Coimbra, Portugal. 
Peherstorfer, Franz. address. Johannes Kepler
Universitat Linz, Linz, Austria. 
Pereira de Sousa,
Victor Luís. address. Instituto Politécnico de Bragança,
Escola Superior de Tecnologia e de Gestão de Bragança, Ap. 134, 5301857 Bragança,
Portugal. 
Pérez Sinusía,
Ester. address. Universidad Pública de Pamplona, Campus de Arrosadía s/n Pamplona 31006,
Spain. 
Petronilho,
José carlos. address. Universidade de Coimbra, Departamento
de Matemática, FCTUC, Apartado 3008, Portugal. 
Postelmans,
Kelly. address. Katholieke Universiteit Leuven, Celestijnenlaan 200 B 3001 Leuven,
Belgium. 
Rebocho,
Maria das Neves. address. Universidade da Beira Interior,
Departamento de Matemática, Av. Marquês D'Ávila e Bolama, 1, Covilhã. 
Salto,
Laura. address. Universidad Carlos III, Ave. Universidad, 30,
28911 LeganésMadrid, Spain. 
SanchezLara,
Joaquin. address. Universidad de Almeria, Crta. de Sacramento s/n. La Cañada 04120. ALMERIA,
Spain. 
SánchezMoreno,
Pablo. address. Universidad de Granada. Instituto "Carlos I" de Física Teórica y
Computacional, Facultad de Ciencias. Campus de Fuentenueva, Spain. 
SánchezRuiz,
Jorge. address. Universidad Carlos III, Ave. Universidad, 30,
28911 LeganésMadrid, Spain. 
Santos,
Ana Margarida. address. Universidade de Aveiro, Departamento
de Matemática, Campus de Santiago, 3810 Aveiro, Portugal. 
Santos Cardoso, José Luis. address. UTAD,
Dep. de Matemática, Quinta de Prados, Apartado 1013, 5000911 VILA REAL. 
Srayeb,
Nadia. address. Faculté de Science de Sfax, I.S.S.A.T Gabes route de
Mednine,
Tunisia. 
Stabolas,
Ioannis. address. University of Patras, Department of Mathematics, University of
Patras, Patras 26500,
Greece. 
Van Assche, Walter. address. Katholieke Universiteit
Leuven, Celestijnenlaan 200 B 3001 Leuven, Belgium. 
Van Doorn, Erik. address. Faculty of Mathematical
Sciences, University of Twente, PO Box 217, 1500 AE Enschede, The
Netherlands. 
Vanlessen,
Maarten. address. Katholieke Universiteit Leuven, Celestijnenlaan 200 B 3001
Leuven,
Belgium. 
Wielonsky,
Franck. address. Universite des Sciences et Technologies de Lille 1,
UFR de Mathematiques, Bat. M3, USTL, 59655 Villeneuve d'Ascq cedex,
France. 
Wozny,
Pawel. address. Institute of Computer Science University of Wroclaw,
ul. Przemyckiego 20, 51151 Wroclaw, Poland. 
Yakubovich,
Semyon. address. Departamento de
Matemática Pura da Universidade do Porto, Porto, Portugal. 
Zygmunt,
Marcin Jakub. address.
Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4,
Poland. 

For further questions please contact
Amílcar Branquinho
or Ana Foulquié. 

With
support from
SOCRATES
Programme
"Orthogonal Polynomials and Special Functions" ref.
29242IC12001PTERASMUSIP13,
CMUC (Centro de
Matemática da Universidade de Coimbra), FCT
(Fundação para a Ciência e Tecnologia),
and the
SIAG (SIAM Activity Group on
Orthogonal Polynomials and Special Functions). 

