9th European Workshop on Applications and Generalizations of Complex Analysis

Centro Internacional de Matemática, Coimbra, Portugal

July 1, 2006

Annoucement
Work Program
Abstracts
List of Participants
Support
Annoucement

Dear Colleagues,

It is with great pleasure that we invite you to participate in the "9th Workshop on Applications and Generalizations of Complex Analysis",  to be held at the International Center for Mathematics, on July 1st, 2006.  As usual, we will have talks of about 25 minutes plus 5 minutes discussion. We  would be very glad if you would decide to participate and even more to  present a contribution. This workshop is satellite to the "12th European Intensive Course on Complex Analysis and Applications to Partial Differential Equations" to be held in both Universities of Coimbra and Aveiro from June 26 to July 7, 2006.
This intensive course is intended to celebrate the long lasting co-operation between the involved Universities.  Students and Lecturers from almost a dozen European countries participated in the past and we hope that  this will also continue in the future. We kindly ask all of you which kept in touch with former participants  to forward them this message.
This workshop is intended to give an opportunity for discussions between junior and senior researchers from several european countries in various fields of mathematics related to Complex, Quaternionic and Clifford Analysis, like Algebra, Geometry, Numerical Analysis, Differential Equations, and Special Functions.
For more informations, please go to http://www.mat.uc.pt/~ajplb/12.htm and http://www.cim.pt/?q=aboutcim. Besides a formal inscription by replying to this announcement there will be no fee. We are able to offer some grants for accommodations and/or lunches for students or junior scientist participants. Requests should be send to Amílcar Branquinho (ajplb@mat.uc.pt) with the following data:
Name:
Affiliation:
I intend to participate in the Intensive Course: Yes/No
I intend to participate in the Workshop with a communication ___ / without a communication __
Tentative title:
I need an invitation letter: _____; for that purpose, contact me via the e-mail:____________or by fax:_______________________
I need help with accommodation in Coimbra or Aveiro:_______;
Please send as soon as possible a short abstract of your communication (in Latex, at most 10 lines).
Looking forward to meet you.
The Organizers,
Amilcar Branquinho (Departamento de Matemática Universidade de Coimbra)
Ana Foulquié (Departamento de Matemática da Universidade de Aveiro)
Jaime Carvalho e Silva (Departamento de Matemática Universidade de Coimbra)
Maria Isabel Cação (Departamento de Matemática da Universidade de Aveiro)

Morning Session

Afternoon Session

9:30-9:45  Opening Session 14:30-14:55  Andrei Martinez Finkelshtein
9:45-10:10  Eduardo Godoy 15:00-15:25  Luís Cotrim
10:15-10:40  Maria das Neves Rebocho 15:30-15:55  Abey López
10:45-11:10  Roberto Costas-Santos 16:00-18:00  Coffee Break
11:15-11:30  Coffee Break 18:00-18:25  Francisco Lage Calheiros
11:30-11:55  Nelson Vieira 18:30-18:55  Rui Marreiros
12:00-12:25  Ricardo Gonçalves Pereira 19:00-19:25  David Kapanadze
12:30-12:55  Regina de Almeida 19:30-19:55  Giorgi Boveradze

Lunch take place at CIM from 13:00 til 14:30

Author: Francisco Marcellán --- cancelled

program

Title: When linear combinations of orthogonal polynomials yield new families of orthogonal polynomials?
Abstract: In this talk a survey of recent results about analytic and algebraic properties of quasi-orthogonal polynomial sequences of order k (a linear combination of k consecutive elements of a sequence of orthogonal polynomials) will be presented. More precisely, we will focus our attention in the study of necessary and sufficient conditions in order to a sequence of quasi-orthogonal polynomials becomes orthogonal when the coefficients in the linear combination are constant real numbers.
This is a joint work with M. Alfaro, A. Peña, and M.L. Rezola (Departamento de Matematicas, Universidad de Zaragoza, Spain).
Author: Maria das Neves Rebocho

program

Title: First order structure relations for orthogonal polynomials on the unit circle.
Abstract: This talk is concerned with structure relations (differential relations) for orthogonal polynomials on the unit circle. Let Φn be a sequence of orthogonal polynomials on the unit circle, orthogonal with respect to a functional whose corresponding Carathéodory function, F, satisfies a first order differential equation with polynomial coefficients.
In this talk we will present a characterization of Φn of orthogonal polynomials on the unit circle associated with a Carathéodory function, F, which satisfies a first order differential equation, in terms of first order structure relations. This result is a generalization of a known result for sequences of orthogonal polynomials on the real line, namely the equivalence between (some specific) first order structure relations and the semi-classical character of these sequences.
This result is a generalization of a result established for orthogonal polynomials Also, we will deduce orthogonality properties of Φn, and we will discuss the semi-classical character of Φn.
Author: Eduardo Godoy

program

Title: The structure relations and difference representations for orthogonal polynomials of hypergeometric
type in two discrete variables.
Abstract: In [1], we provided a method for constructing orthogonal polynomials of two discrete variables on a simplex, giving a system
of two independent recurrence relations in vector--matrix form, their second order partial difference equation, structure relations and some limit relations between some bivariate families (Hahn, Meixner, Kravchuk and Charlier) obtained using the method.
Motivated by the recent paper [2] where a systematic study of the orthogonal polynomial solutions of a second order partial difference equation of hypergeometric type of two variables was done and from the classification of the admissible equations of hypergeometric type, we have obtained an explicit difference derivative representation and structure relations for orthogonal polynomials of hypergeometric type in two discrete variables. This is explicitly discussed for bivariate Hahn, Meixner, Kravchuk and Charlier polynomials.
[1] J. Rodal, I. Area and E. Godoy. Orthogonal polynomials of two discrete variables on the simplex. Integral Transforms and Special Functions 16 (3), 263--280 (2005).
[2] J. Rodal, I. Area and E. Godoy. Linear partial difference equations of hypergeometric type: orthogonal polynomial solutions in two discrete variables. Journal of Computational and Applied Mathematics (2006) (in press).
Author: Nelson Vieira

program

Title: Non-stationary Schroedinger equation in Clifford Analysis
Abstract: We consider a factorization of the non-stationary Schroedinger operator based on the parabolic Dirac operator introduced by Cerejeiras, Kähler, and Sommen. Based on the fundamental solution for the parabolic Dirac operators, we shall construct an appropriated Teodurescu operator. Afterwards we will describe how to solve the nonlinear Schroendinger equation using Banach fixed point theorem. Special emphasize will be given to the convergence of the numerical scheme.
Author: Ricardo Gonçalves Pereira

program

Title: Determinant of quaternionic polynomial matrices
Abstract: After introducing the skew field of quaternions, the Dieudonné determinant of quaternionic matrices is presented. Then we give some notions on quaternionic polynomials and polynomial matrices and we define a polynomial determinant of such matrices. Finally, we show the relation between this determinant and the eigenvalues of companion matrices.
Author: Regina de Almeida

program

Title: On the Growth of Polymonogenic Functions
Abstract: We study the growth of entire Clifford algebra valued solutions of the iterated Dirac equation and also entire solutions of the iterated generalized Cauchy-Riemann equation in higher dimensional Euclidean space. These classes of functions are denoted as polymonogenic or k-monogenic functions. We start by developing a sharp Cauchy-type estimate for polymonogenic functions. Then using the maximum modulus, maximum term of the Taylor-Almansi series expansion and central index we obtain generalizations of some results due to Wiman-Valiron. Applying these results we establish asymptotic relations between the growth of solutions to these systems of partial differential equations and that of their iterated Euler and Gamma operators.
Joint work with D. Constale and R.S. Krauβhar Department of Mathematical Analysis, Ghent University.
Author: Andrei Martinez Finkelshtein

program

Title: Asymptotics of Szegö polynomials for the analytic weight: the Riemann-Hilbert aproach
Abstract: We discuss some results about the asymptotic distribution of zeros and the behavior of relevant coefficients of the polynomials orthogonal on
the unit circle that can be obtained via the Riemann-Hilbert technique assuming that the orthogonality weight is sufficiently analytic.
Author: Luís Cotrim

program

Title: Algebraic theory of multiple orthogonal polynomials
Abstract: In this talk we present the general theory of multiple orthogonal polynomials. Our departure point is the three term recurrence relation, with matrix coefficients, satisfied by a sequence of vectors polynomials. Connection with the operator theory and construtive theory of approximation are presented. Comparisons with the cases studied from the article of A.I. Aptekarev and A. Branquinho and W.Van Assche, Multiple Orthogonal Polynomials for Classical Weights, Transactions of the American Mathematical Society, vol. 335, n. 10 (2003), 3887-3914, will also be presented.
Author: Abey Lopez García

program

Title: Ratio asymptotic of multiple orthogonal polynomials.
Abstract: We prove ratio asymptotic for multiple orthogonal polynomials with respect to a Nikishin system of measures µ1, ..., µm whose supports consists of an interval on which µm' > 0 almost everywhere plus a denumerable set of mass points. This results is an extension of the Rakhmanov-Denisov Theorem.
Author: Roberto Costas-Santos

program

Title: Limit relations between q-Krall type orthogonal polynomials.
Abstract: In this talk, we consider a natural extension of several papers related to Krall-type polynomials  introducing  a modification of a q-classical linear operator via the addition of one or two mass points. The limit relations between the q-Krall type modification of big q-Jacobi, little q-Jacobi, big q-Laguerre, and other families of the q-Hahn tableau is established.
Author: Francisco Calheiros

program

Title: Complex analysis of real systems
Abstract: Froissart doublets diffusion on the sea surface (Leixões), thinking with analytical properties Bipartition method on the Plan. Final statement: Why engineering students must study complex analysis.
Author: Rui Marreiros

program

Title: On the kernel of some singular integral operators with non-Carleman shift.
Abstract:  We will consider the operator T=I - cUP+: L2n T → L2n T, on the unit circle T, with a non-Carleman shift α : TT which has a finite set of fixed points, and where I is the identity operator, c in Cnxn(T) is a continuous matrix function,  (U \varphi ) (t)=\sqrt{ | α'(t) | } \varphi (α (t))  is the isometric shift operator and P±= 1/2 (I± S)$ are the complementary projection operators, with (S\varphi ) (t)=(π i)-1 \int_{T} \varphi (\tau )(\tau-t)^{-1}d\tau  the operator of singular integration with Cauchy kernel. It is supposed that all the eigenvalues of the matrix c (t) at the fixed points of the shift, simultaneously belong either to the interior of the unit circle T or to its exterior. Under these and related conditions, estimates for the dimension of the kernel of the operator T, defined on the unit circle or on the one point compactification of the real line, are obtained.
Author: David Kapanadze

program

Title: On the impedance wave diffraction problems
Abstract: We investigate the impedance wave diffraction problems. Using the potential method, from the original boundary value problem we derive systems of integral equations which will translate the initial problem. The main result culminates with the invertibility of the corresponding matrix pseudo-differential operators in appropriate function spaces.
Author: Giorgi Boveradze

program

Title: The Fredholm property for Wiener-Hopf-Hankel operators in L2 Lebesgue spaces
Abstract:  We will present a study of the Fredholm property for Wiener-Hopf plus/minus Hankel operators with piecewise almost periodic Fourier symbols, and acting between L2 Lebesgue spaces. The study is based on certain special factorizations of the corresponding Fourier symbols of the operators. Some examples are provided in view of the results illustration.
List of participants

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Almeida, Regina de. address. Universidade de Trás-os-Montes e Alto Douro. e.mail. ralmeida@utad.pt.
Alzugaray, Maria Teresa. address.Department of Mathematics, Grant Campus, Suffolk County Community College, Brentwood, NY 11717, USA. e.mail. rodrigma@sunysuffolk.edu.
Bernardes, Gil. address. Departamento de Matemática da Universidade de Coimbra, Apartado 3008, 3000 Coimbra, Portugal. e.mail. gilb@mat.uc.pt.
Bock, Sebastian. address. Bauhaus-Universität Weimar, Germany. e.mail. bastian.bock@web.de.
Boveradze, Giorgi. address. Universidade de Aveiro, Departamento de Matemática, Campus de Santiago, 3810-193, Aveiro, Portugal. e.mail.
Calheiros, Francisco. address FEUPorto e.mail.jolacam@netcabo.pt.
Carvalho, José Manuel. address. Departamento de Matemática da Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, 2829-516, Monte da Caparica.e.mail. jmprc@netcabo.pt.
Cerejeiras, Paula. address. Universidade de Aveiro, Departamento de Matemática, Campus de Santiago, 3810-193, Aveiro, Portugal.
Costa, Cecília. address. Departamento de Matemática da Universidade de Trás-os-Montes e Alto Douro. e.mail. mcosta@utad.pt.
Costas Santos, Roberto. Universidad Carlos III de Madrid, Spain. e.mail. rcostas@math.uc3m.es.
Cotrim, Luís. address. Escola Superior de Tecnologia e Gestão do I.P.L., Quinta do Seixo lote 1 - 4 Dto, 2410 Leiria, Portugal. e.mail.  lmsc@estg.ipleiria.pt.
Coutinho, Cláudia. address. Universidade de Aveiro, Portugal. e.mail. claudia.coutinho@mat.ua.pt.
Falcão, Irene. address. Departamento de Matemática da Universidade do Minho, Campus de Gualtar, 4710-057 Braga.e.mail. mif@math.uminho.pt.
Faustino, Nelson. address. Universidade de Aveiro, Portugal. e.mail. nfaust@mat.ua.pt.
Ferreira, Mílton. address. Universidade de Aveiro, Portugal. e.mail. mferreira@mat.ua.pt.
Garza Gaona, Luis Enrique. address. Universidad Carlos III de Madrid, Spain. e.mail. luisgarzagaona@hotmail.com.
Godoy, Eduardo. address. Departamento de Matemática Aplicada II, E.T.S. Ingenieros de Telecomunicación, Universidad de Vigo, Campus de Lagoas-Marcosende, 36310-Vigo, Spain. e.mail. egodoy@dma.uvigo.es.
Jesus, Márcio Dinis do Nascimento de. address. Instituto Politecnico de Viseu, Escola Superior e Tecnologia de Viseu. e.mail. mnasce@mat.estv.ipv.pt.
Kähler. address. Universidade de Aveiro, Departamento de Matemática, Campus de Santiago, 3810-193, Aveiro, Portugal.
Kapanadze, David. address. Universidade de Aveiro, Departamento de Matemática, Campus de Santiago, 3810-193, Aveiro, Portugal. e.mail. daka@rmi.acnet.ge , david.kapanadze@gmail.com
López García, Abey. address. Universidad Carlos III de Madrid, Spain.e.mail.abey.lopez@Vanderbilt.Edu.
López Lagomasino, Guillermo. address. Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés-Madrid, Spain. e.mail. lago@math.uc3m.es.
Malonek, Helmuth. address. Departamento de Matemática, Universidade de Aveiro, Campus de Santiago, 3810 Aveiro, Portugal. e.mail. hrmalon@mat.ua.pt.
Martinez-Finkelshtein, Andrei. address. Dept. Estadistica y Matematica Aplicada, Universidad de Almeria, La Canada, 04120 Almeria, Spain. e-mail. andrei@ual.es.
Marreiros, Rui. address. Departamento de Matemática, FCT, Universidade do Algarve, Gambelas, 8005-139 Faro, Portugal,  e-mail.rmarrei@ualg.pt.
Matos, José. address. Departamento de Matemática, Instituto Superior de Engenharia. e.mail. jma@isep.ipp.pt.
Mendes, Ana Isabel. address. Escola Superior de Tecnologia e Gestão do I.P.L., Quinta do Seixo lote 1 - 4 Dto 2410 Leiria, Portugal. e.mail. aimendes@estg.ipleiria.pt.
Nunes, Luis. address. Departamento de Matemática, Universidade de Aveiro, Campus de Santiago, 3810 Aveiro, Portugal.
Pereira, Ricardo Jorge Aparicio Gonçalves. Universidade de Aveiro, Departamento de Matemática, Campus de Santiago, 3810-193, Aveiro, Portugal. e.mail. ricardo@mat.ua.pt.
Pereira de Sousa, Vitor Luís. address. Instituto Politécnico de Bragança, Escola Superior de Tecnologia e de Gestão de Bragança, Ap. 134, 5301-857 Bragança, Portugal. e.mail. vitorsousa@ipb.pt.
Petronilho, José Carlos. address. Departamento de Matemática da Universidade de Coimbra, Apartado 3008, 3000 Coimbra, Portugal. e.mail. josep@mat.uc.pt.
Prieto, Ulises Fidalgo. address. Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés-Madrid, Espanha. e.mail. ulisesfidalgoprieto@yahoo.es.
Rebocho, Maria das Neves. address. Universidade da Beira Interior, Departamento de Matemática, Av. Marquês D'Ávila e Bolama, 1, Covilhã. e.mail. mneves@noe.ubi.pt.
Robalo, Tânia. address. Departamento de Matemática, Universidade de Aveiro, Campus de Santiago, 3810 Aveiro, Portugal.
Tomaz, Graça Maria de Oliveira. address.  Escola Superior de Tecnologia e Gestão, IPG, Portugal.e.mail.gtomaz@ipg.pt.
Vettori, Paolo. address. Universidade de Aveiro, Departamento de Matemática, Campus de Santiago, 3810-193, Aveiro, Portugal.
Vieira, Nelson Felipe Loureiro. address. Universidade de Aveiro, Departamento de Matemática, Campus de Santiago, 3810-193, Aveiro, Portugal. e.mail. nvieira@mat.ua.pt.
Vitória, José da Silva Lourenço. address. Departamento de Matemática da Universidade de Coimbra, Apartado 3008, 3000 Coimbra, Portugal.
Sponsors

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With support from Centro de Matemática da Universidade de Coimbra, UI&D "Matemática e Aplicações" do Universidade de Aveiro, Centro Internacional de Matemática and the Socrates programme. Centre for Mathematics, University of Coimbra