The Institute of Mathematics of the University of Barcelona (IMUB) organizes a workshop on
Wavelets and Applications, July 16, 2002 (Barcelona). The Organizing Committee is:
María J. Carro, Joan Cerdà, Joaquim Martín, and Javier Soria. The course is addressed to graduate students and young researchers not necessarily specialized on wavelets. 

There will be four main basic courses:  Introduction and basic aspects of wavelets theory, G. Weiss (PDF ).  Wavelets and probability, R. Gundy (PDF ).  Wavelets and numerical methods, C. Canuto and A. Tabacco (PDF, Slides 1, Slides 2, Slides 3 ).  Computerbased wavelet analysis, T. Nguyen (PDF ). The workshop will also consist of several specialized lectures related and complementing the above courses. (The workshop Lecture Notes, published by the IMUB, can be downloaded in PDF format.) 
The lectures will take place at the Faculty of Mathematics building, located at the downtown campus of the University of Barcelona.
The registration fee is 90 € (EUROS). Due to restrictions in the use of computer laboratories, the number of participants is limited (there will be two laboratory groups, each having two different sessions. See the Programme for more details). The inscription will be done by rigorous date of payment.
With the support of the Spanish Mathematical Society (RSME), the organizers will offer a few grants to cover some of the participants expenses. This money will be awarded directly by the RSME after the workshop.
On Thursday, July 4, there will be an organized tour through Barcelona. This activity is supported by the City Council and it is free for the participants.
On Friday, July 5, we will have a special dinner on the Escola d'Hostaleria de Barcelona.
If you need help for booking your hotel room, check the information available at the ACCOMMODATION FORM. Please address all questions you may have on this matter to the Congress Office of the University of Barcelona.
To obtain more information about the city of Barcelona you may want to visit the web site of the City Council or the web site of Tourism in Barcelona. You can also consult an interactive map of Barcelona or check the weather forecast.
MONDAY, July 1
9:0010:30 Reception
10:3011:00 Welcoming address
11:0012:00 Introduction and basic aspects of wavelets theory (1)
12:0013:00 Wavelets and numerical methods (1)
13:0015:00 Lunch
15:0016:00 Wavelets and probability (1)
16:0017:00 Eugenio Hernández (U. Autonóma de Madrid): Nonlinear approximation and wavelets (PDF )
TUESDAY, July 2
9:3010:30 Computerbased wavelet analysis
10:3011:30 Wavelets and probability (2)
11:3012:00 Break
12:0013:00 Introduction and basic aspects of wavelets theory (2)
13:0015:00 Lunch
15:0016:00 Wavelets and numerical methods (2)
16:0017:00 Miquel Ralló (Laboratori de Processat d'Imatges, UPC): Wavelet based techniques for textile inspection (PDF )
WEDNESDAY, July 3
9:0010:30 Computerbased wavelet analysis (Lab. session 1)
10:3011:00 Break
11:0012:00 Wavelets and probability (3)
12:0013:00 Introduction and basic aspects of wavelets theory (3)
13:0015:00 Lunch
15:0016:00 Wavelets and numerical methods (3)
16:1517:45 Computerbased wavelet analysis (Lab. session 1)
THURSDAY, July 4
9:3010:30 Edward Wilson (Washington U.): The algebra of shift invariant spaces and applications to wavelet theory (PDF )
10:3011:30 Hrvoje Sikic (U. Zagreb): Tight frame wavelets and the dimension function (PDF )
11:3012:00 Break
12:0013:00 Wavelets and numerical methods (4)
13:0015:00 Lunch
15:0018:00 Organized tour through Barcelona
FRIDAY, July 5
9:0010:30 Computerbased wavelet analysis (Lab. session 2)
10:3011:00 Break
11:0012:00 Wavelets and probability (4)
12:0013:00 Introduction and basic aspects of wavelets theory (4)
13:0015:00 Lunch
15:0016:00 Wavelets and numerical methods (5)
16:1517:45 Computerbased wavelet analysis (Lab. session 2)
21:0023:00 Special dinner
SATURDAY, July 6
9:3010:30 Claudio Canuto (Politecnico di Torino): Waveletbased analysis of singular perturbation problems (PDF )
10:3011:30 Wavelets and probability (5)
11:3012:00 Break
12:0013:00 Introduction and basic aspects of wavelets theory (5)
 Introduction and basic aspects of wavelets theory (Guido Weiss , Washington University) (PDF ).
We begin with a general description of reproducing systems on n dimensional Euclidean space; this will include both the continuous and discrete cases. We then will proceed to give a unified approach for the study of all these collections. The first goal will be to present a theorem that characterizes all such systems. Particular special cases are wavelets (in all dimensions, finitely generated, with very general dilations), Gabor systems and Gaborlike systems, the frame versions of these systems and others that are more general. Many concrete examples will be constructed. Other topics that are related to this that will be discussed are: shift invariant subspaces, connectivity properties of these systems, oversampling.
 Wavelets and probability (Richard Gundy, Rutgers University) (PDF ).
In these lectures, we want to illustrate some connections between wavelet analysis and probability. The emphasis will be in the direction from probability to wavelet analysis, rather than the other way. At this point, we have two principal topics in mind:
 Wavelets and numerical methods (Claudio Canuto and Anita Tabacco, Politecnico di Torino) (PDF, Slides 1, Slides 2, Slides 3 ).
The theory, design and application of wavelets will be discussed in the course with emphasis on computerbased laboratory use. Topics to be discussed and demonstrated are multiresolution analysis; design of different wavelet types; image compression and signal denoising. The course consists of a lecture session followed by two handon PCbased laboratory sessions.
D. Gundy, C. Canuto, E. Wilson, G. Weiss, H. Sikic E. Hernández, A. Tabacco, T. Nguyen 
IMUB
University of Barcelona
Gran Via 585
08071 Barcelona, Spain
Fax: 3493 403 5963
wavelets@imub.ub.es