With the support of Centro de Matemática da Universidade de Coimbra and INTAS project ref. 00-272 .
The meeting take place in room Anastácio da Cunha of Mathematical Department of Coimbra University.
February 7: visit to the University of Coimbra
February 8: visit to the Mathematical Department library; Conference
Dinner
The participants stay in Residenciais Alentejana, Antunes and Botânico.
| 7-02-2002 | 8-02-2002 | 9-02-2002 | |
| 9h30m-10h30m | × | Kaliaguine | × |
| 10h30m-11h | × | Castro/Durán | meeting |
|
11h-11h30m
|
opening session
|
meeting
|
|
| 11h30m-12h | Stahl | Marcellán | closing session |
| 12h-12h30m | --×-- | Martinez Finkelshtein | × |
| 12h30m-15h | lunch/visit | lunch/visit | lunch |
| 15h-16h | Van Assche | Aptekarev | × |
|
16h-16h30m |
Beckerman | Van Iseghem | × |
| 16h30m-17h | Arvesu | Kuijlaars | × |
| 17h-17h30m | Buyarov | López Lagomasino | × |
|
17h30m-19h |
workshop seminar
|
workshop seminar
|
×
|
| 19h | × | Dinner | × |
Author: Herbert Stahl
Title: Hermite-Padé Polynomials and Algebraic Approximants to the Exponential Function
Abstract: Results about Hermite-Padé polynomials and algebraic approximants
to the exponential function will be reviewed. Special emphasis is
given to the asymptotic distribution of the zeros of Hermite-Padé
polynomials and the definition of a Riemann surface which is pivotal
in the description of the asymptotic behavior of the polynomials, its
zeros, and the error function of the algebraic approximants associated
with the exponential function. We shall report about new results,
which are part of the coordinated activities of the INTAS project.
Author: Alexander Aptekarev
Title: Strong asymptotics for polynomials orthogonal with respect to a complex varying weight and applications to the best rational approximation
Abstract: We discuss application of methods based on boundary value problems
for analytic functions (Riemann-Hilbert problem) to the asymptotics
of complex orthogonal polynomials. Statements of two theorems in this
direction will be considered in details. These theorems are the key tool
for obtaining the sharp constants for the rate of approximation by rational
functions of some general class of analytic functions, which includes
exp, log and sqrt.
Author: Andrei Martinez Finkelshtein
Title: Electrostatics for the zeros of classical polynomials revisited
Abstract: This is a preliminary report on the progress of the electrostatic
interpretation of the zeros of some classical polynomials, which
avoids an a priori restriction on the location of the zeros. It is
shown that the zeros solve certain min-max problem for the logarithmic
energy, extending (in some since) to the discrete setting the well-known
symmetry of the compact of min capacity, described by H. Stahl.
Only the simplest case of Jacobi polynomials with parameters
>-1 will be considered; although the proof still presents some
gaps, its present state makes it worth to be discussed.
Author: Arno Kuijlaars
Title: The relativistic Toda lattice
Abstract: The relativistic Toda lattice is a generalization of the ordinary
Toda lattice introduced by S. Ruijsenaars in 1990. It is well-known
that the finite, non-periodic Toda lattice is related to spectral theory
of tridiagonal matrices and orthogonal polynomials. I will discuss an
analogous relation in the relativistic case with spectral theory for
a pair of bidiagonal matrices and Laurent orthogonal polynomials.
This is work in progress with Jonathan Coussement and Walter Van
Assche (both at K.U.Leuven).
Author: Walter Van Assche
Title: Quadratic Hermite-Pad\'e approximation to the exponential function: a Riemann-Hilbert approach
Abstract: We investigate the asymptotic behavior of the polynomials $p,q,r$
(with degrees respectively $n_1,n_2,n_3$) in type I Hermite-Pad\'e
approximation to the exponential function, i.e., $p(z)e^{-z} +q(z)
+ r(z) e^z = \mathcal{O}(z^{n_1+n_2+n_3+2})$ as $z \to 0$. We use a
Riemann-Hilbert approach for $3\times 3$ matrix valued functions. An
important role is played by a three-sheeted Riemann surface and certain
rational functions defined on it. We show how to transform the Riemann-Hilbert
problem and how a deformation of the contours allows us to obtain asymptotics
for the polynomials $p,q,r$. As a result, we obtain results on the behavior
of the zeros of these polynomials.
Author: Vladimir Buyarov
Title: Some open problems in the theory of continued fraction
Abstract: We will discuss an approach to some open problem of Gonchar
about discs of meromorphicity for continued C-fraction with randomly chosen
coefficients of value +1 and -1.
Author: Jeannette Van Iseghem
Title: Vector QD algorithm and vector continued fractions
Abstract: Continued fractions and QD algorithm: scalar, vector and matrix
cases.
Author: Jorge Arvesu
Title: Discrete Multiple Orthogonal Polynomials
Abstract: The talk deals with Discrete Multiple Orthogonal Polynomials.
Special attention will paid to the q-Hermite-Padé polynomials. Some algebraic
and analytical properties of the q-multiple orthogonal polynomials are
shown. Finally, one example of q-Hermite-Padé polynomial is given.
Author: Francisco Marcellán
Title: Freud-Sobolev Orthogonal Polynomials. Asymptotic properties
Abstract: We introduce orthogonal polynomials with respecto to a Sobolev
inner product involving the first derivatives where the measure is associated
with the weight function exp -x4 coinsidered among others by G. Freud and
P. Nevai. In particular we study some algebraic and analytic properties of
such polynomials. A Plancherel-Rotach asymptotic formula is obtained.
Author: Guillermo López Lagomasino
Title: Stieltjes polynomials with respect to varying weigths
Abstract:
Author: António Durán and Mirta Castro
Title: Boundedness properties for Sobolev inner products
Abstract: The work deals with Sobolev orthogonal polynomials. Sobolev
orthogonality is written in terms of matrix orthogonality, involving differential
operators. Particularly, it is explored the connection bettween some boudedness
properties for the support of the measures appearing in the Sobolev inner
product and the set o zeros of the orthogonal polynomials, completing previous
results in this area.
Author: Bernhard Beckermann
Title: The (discrete) Zolotarev Problem and its applications to best rational approximation and to eigenvalue estimates for Hankel matrices
Abstract: Recently, some approximately sharp upper bounds were given for
the ratio of the smallest over the largest eigenvalue of any positive definite
Hankel matrix. In the present talk we present similar results for the
ratio of two eigenvalues of a positive definite Hankel matrix. This enables
us to derive lower bounds for the condition number of any (not necessarily
positive definite) Hankel matrix in terms of its signature.
A main tool in our investigations is some extremal problem in logarithmic
potential theory, namely a condenser with a maximum charge constrain.
Author: Victor I. Buslaev
Title: A counter example to the Padé conjecture
Abstract: Recently D. Lubinsky has obtained a counter-example for long
standing conjecture of Backer-Gammel-Wills (or the so called Padé-conjecture).
His counter-example related to the so called meromorphic case of the
conjecture. We shall speak about another new example related to the
``holomorphic´´ case of the conjecture. Thus a function holomorphic in
a circle such that any subsequence of its diagonal Padé approximation
does not converge locally uniformly inside the circle, will be presented.
Author: Valeri Kaliaguine
Title: On compact perturbation of band operators
Abstract: We will discuss about inversion of Weyl criterion of compact
perturbation of operators. Thus, we consider a problem whether adding
to the spectral measure of a Jacobi or band operator discrete masses,
we get or not a compact perturbation of operator.
Alexander Ivanovich Aptekarev - Russian Academy of Sciences, Keldysh
Institute of Applied Mathematics, Miusskaya Square 4, 125047 Moscow,
RUSSIA
e.mail: aptekaa@rfbr.ru
Accomodation: Residencial Antunes
Alexandra Nascimento - Instituto Politécnico de Leiria, Leiria, PORTUGAL
e.mail: xana_nascimento@hotmail.com
Accomodation: Residencial Antunes
Amílcar Branquinho - Departamento de Matemática da Universidade de
Coimbra, 3000 Coimbra, PORTUGAL
e.mail: ajplb@mat.uc.pt
Ana Filipa Soares Loureiro - ISEC, Coimbra, PORTUGAL
e.mail: anafsl@isec.pt
Ana Foulquié Moreno - Departamento de Matemática da Universidade de
Aveiro, 3810-193 Aveiro, PORTUGAL
e.mail: foulquie@mat.ua.pt
Ana Isabel Mendes - Instituto Politécnico de Leiria, Leiria, PORTUGAL
e.mail: aimendes@yahoo.com
Ana Margarida Santos - Departamento de Matemática da Universidade de
Aveiro, 3810-193 Aveiro, PORTUGAL
e.mail: @
Anabela Monteiro Paiva - Departamento de Matemática da Universidade
da Beira Interior, 6200 Covilhã, PORTUGAL
e.mail: apaiva@noe.ubi.pt
Accomodation: Residencial Antunes
André Draux - INSA de ROUEN, Rouen, FRANCE
e.mail: draux@lmi.insa-rouen.fr
Accomodation: Residencial Botânico
Andrei Martinez Finkelshtein - Departamento de Estadística y Matemática
Aplicada, Universidad de Almería, 04120 Almería, SPAIN
e.mail: andrei@ual.es
Accomodation: Residencial Botânico
Antonio José Durán Gardeño - Universidad de Sevilla, SPAIN
e.mail: duran@us.es
Accomodation: Residencial Antunes
Arno B. J. Kuijlaars - Department of Mathematics, Katholieke
Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven (Heverlee),
BELGIUM
e.mail: Arno.KUIJLAARS@wis.kuleuven.ac.be
Accomodation: Residencial Alentejana
Bernhard Beckermann - Université de Lille 1, Laboratoire d'Analyse Numérique
et d'Optimisation, Cité Scientifique, F-59655 Villeneuve d'Ascq,
FRANCE
e.mail: bbecker@ano.univ-lille1.fr
Accomodation: Residencial Antunes
Claude Brezinski - Université de Lille 1, Laboratoire d'Analyse Numérique
et d'Optimisation, Cité Scientifique, F-59655 Villeneuve d'Ascq,
FRANCE
e.mail: Claude.Brezinski@univ-lille1.fr
Accomodation: Residencial Botânico
Christian Berg - K\obenhavns Universitet, Copenhagen, DENMARK
e.mail: BERG@math.ku.dk
Accomodation: Residencial Antunes
Elisabete Sousa Almeida - Instituto Politecnico de Viseu, Viseu, PORTUGAL
e.mail: betty@mat.estv.ipv.pt
Accomodation: Residencial Antunes
Francisco Marcellán Español - Departamento de Matemáticas, Universidad
Carlos III de Madrid, 28911 Leganés-Madrid, SPAIN
e.mail: pacomarc@ing.uc3m.es
Accomodation: Residencial Alentejana
Guillermo López Lagomasino - Departamento de Matemáticas, Universidad
Carlos III de Madrid, 28911 Leganés-Madrid, SPAIN
e.mail: lago@math.uc3m.es
Accomodation: Residencial Alentejana
Helmuth R. Malonek - Departamento de Matemática da Universidade de Aveiro,
3810-193 Aveiro, PORTUGAL
e.mail: hrmalon@mat.ua.pt
Herbert Stahl - Technische Fachhochschule Berlin, Fachbereich II, Luxemburgerstrasse
10, D-13353 Berlin, GERMANY
e.mail: stahl@tfh-berlin.de
Accomodation: Residencial Botânico
Jaime Carvalho e Silva - Departamento de Matemática da Universidade de
Coimbra, 3000 Coimbra, PORTUGAL
e.mail: jaimecs@mat.uc.pt
Jeannette Van Iseghem
- Université de Lille 1, Laboratoire d'Analyse Numérique et
d'Optimisation, Cité Scientifique, F-59655 Villeneuve d'Ascq, FRANCE
e.mail: jvaniseg@ano.univ-lille1.fr
Accomodation: Residencial Antunes
Jorge Arvesú Carballo - Departamento de Matemáticas,
Universidad Carlos III de Madrid, 28911 Leganés-Madrid, SPAIN
e.mail: jarvesu@math.uc3m.es
Accomodation: Residencial Antunes
Jorge Sánchez-Ruiz
- Departamento de Matemáticas, Universidad Carlos III de
Madrid, 28911 Leganés-Madrid, SPAIN
e.mail: jsanchez@math.uc3m.es
Accomodation: Residencial Antunes
José Carlos Petronilho - Departamento de Matemática da Universidade
de Coimbra, 3000 Coimbra, PORTUGAL
e.mail: josep@mat.uc.pt
Luis Cotrim - Instituto Politécnico de Leiria, Leiria, PORTUGAL
e.mail: lmsc@estg.iplei.pt
Accomodation: Residencial Antunes
Luis Daniel Moura Abreu - Departamento de Matemática da Universidade
de Coimbra, 3000 Coimbra, PORTUGAL
e.mail: daniel@mat.uc.pt
Maria das Neves Vieiro Rebocho - Departamento de Matemática da Universidade
da Beira Interior, 6200 Covilhã, PORTUGAL
e.mail: mneves@noe.ubi.pt
Accomodation: Residencial Antunes
Maria Francisca Matos Cabo - Departamento de Matemática da Universidade
de Coimbra, 3000 Coimbra, PORTUGAL
e.mail: mfmc@mat.uc.pt
Mário António Grande Abrantes - Instituto Politécnico de Bragança,
Bragança, Portugal
e.mail: mar@ipb.pt
Mirta Castro Smirnova - Moscow State University (Moscow - RUSSIA) and
Universidad de Sevilla (Sevilla - SPAIN)
e.mail: mirta@cica.es
Accomodation: Residencial Antunes
Ulises Fidalgo Prieto - Departamento de Matemáticas, Universidad Carlos
III de Madrid, 28911 Leganés-Madrid, SPAIN
e.mail: ufidalgo@math.uc3m.es
Accomodation: Residencial Antunes
Valeri Aleksandrovich Kalyagin (Kaliaguine) - Nizhny Novgorod State
Technical University, Department of Applied Mathematics, Minina Street
24, 603600 Nizhny Novgorod, RUSSIA
e.mail: kalia@waise.nntu.sci-nnov.ru
Accomodation: Residencial Antunes
Victor I. Buslaev -
Steklov Mathematical Institute, Moscow, RUSSIA
e.mail: buslaev@mi.ras.ru
Accomodation: Residencial Antunes
Vladimir S. Buyarov -
Moscow State University, RUSSIA
e.mail: buyarov@math.msu.ru
Accomodation: Residencial Antunes
Walter Van Assche - Department of Mathematics, Katholieke Universiteit
Leuven, Celestijnenlaan 200B, B-3001 Leuven (Heverlee), BELGIUM
e.mail: walter@wis.kuleuven.ac.be
Accomodation: Residencial Alentejana
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