6th European
Intensive Course on Complex Analysis
“Complex
Analysis and its Generalizations (with applications to partial differential
equations)”
Departamento
de Matemática, Universidade de Coimbra, Portugal
With support from CMUC (Centro de Matemática da Universidade de Coimbra), UI&D "Matemática e Aplicaçőes" da Universidade de Aveiro, and the Socrates programme
This intensive course will have a total of 40 hours of lectures and is at postgraduate level. Lecturers will have time available to discuss with the students. Successfully participating students will get a certificate. This course is organized by the Universities of Coimbra and Aveiro with the same goals as the ones organized under the programme Socrates, and is open to all young mathematicians interested in Complex Analysis and its applications.
20 March 
21 March 
22 March 
23 March 
24 March 

9h30m10h 
Opening session 

1012h30m 
Dineen 
Dineen 
Dineen 

Launch Time  
14h 30m17h 
Marcellán 
Marcellán 
Marcellán 
27 March 
28 March 
29 March 
30 March 
31 March 

1012h 30m 
Kisil 
Kisil 
Kisil 

Launch Time 

14h 30m 17h 
Martio 
Martio 
Martio 
• • TENSOR PRODUCTS AND GEOMETRY IN BANACH SPACES  Sean Dineen (Univ. College, Dublin, Ireland)
Abstract:
Introduction to Banach
spaces, HahnBanach theorem, Examples.
Duality theory, weak topology, reflexivity
Bilinear mappings, algebraic tensor
products, linearization, projective and injective tensor products,
examples.
Polynomials and tensor
products.
Polarisation constants and geometric
properties.
Banach algebra, joint spectra, vectorvalued spectra, polynomial
spectral mapping theorems.
•
• ORTHOGONAL RATIONAL FUNCTIONS  Prof. F. Marcellán
(Univ. Carlos III, Madrid, Spain)
Abstract: We will present the state of the art in the subject which constitutes a new and interesting subject of reserach with many applications in Linear Prediction, network synthesis and control theory:
The fundamental spaces
Kernel functions, recurrence and second kind functions
Paraorthogonality and Quadrature
Density of rational functions
Convergence
The boundary case
•
• SPACES OF ANALYTIC FUNCTIONS AND WAVELETS 
Vladimir Kisil (Univ. Leeds, UK)
Abstract: Polynomials Our purpose is to describe a general framework for
generalizations of the complex analysis. As a consequence a classification
scheme for different generalizations is obtained.
The framework is based on wavelets (coherent states) in Banach spaces
generated by “admissible” group representations. Reduced wavelet transform
allows naturally describe in abstract term main objects of an analytical
function theory: the Cauchy integral formula, the Hardy and Bergman spaces,
the CauchyRiemann equation, and the Taylor expansion.
Among considered examples are classical analytical function theories
(one complex variables, several complex variables, Clifford analysis,
SegalBargmann space) as well as new function theories which were developed
within our framework (function theory of hyperbolic type, Clifford version of
SegalBargmann space).
We also briefly discuss applications to the operator theory (functional
calculus) and quantum mechanics.
•
• MODERN TOOLS IN THE THEORY OF QUASICONFORMAL
MAPPINGS  Olli T. Martio (Univ. Helsinki, Finland)
Abstract: The theory of quasiconformal mappings was first developed in
the plane and it was closely connected with the theory of analytic functions
of one complex variable. The standard definitions of quasiconformality are
This intensive course follows the five held in Coimbra and Aveiro from 1995 to 1999 and there are plans for intensive courses in the following years. The lecture notes of some of the courses have been published in Coimbra and others are in print (for more information please see the URL http://www.mat.uc.pt/publicacoes/textosB.html)
Informations about the Mathematics Department or the University of Coimbra can be seen in http://www.mat.uc.pt
Helmuth Malonek (Departamento de Matemática da Universidade de Aveiro)
J. Carvalho e Silva (Departamento de Matemática Universidade de Coimbra)
Amilcar Branquinho (Departamento de Matemática Universidade de Coimbra)