[Turkmath:6888] Octavian Agratini,AIBU

[cenap ozel]

Degerli Liste Uyeleri, 

Babeş - Bolyai Universitesinden Prof Dr Octavian Agratini
Abant Izzet Baysal Universitesi Matematik Bolumunu 1-7 Nisan tarihlerinde
Erasmus kapsaminda ziyaret edecektir. 

Profesor Agratini bu donemde asagida detaylari verilmis konusmalari 
verecektir. 

İlgilerinize saygilarimla arz ederim. 


Cenap Ozel 


Title: SWIMMING IN A SEA OF WAVELETS
Spekaer: Octavian Agratini
Babeş - Bolyai University, Faculty of Mathematics and Computer Science,
Department of Applied Mathematics, 400084 Cluj, Romania
Date:02/04/2010, 15.30 

Abstract of the conference: 


The talk should be considered as an introduction to the fertile field of 
wavelet analy-sis. Wavelets are a tool with a rich mathematical content and 
a great potential for varied applications. For the definition of orthogonal 
wavelet function we follow the direction due to Franklin and Stromberg. 
During exposure we try to give answers to the questions: What are wavelets 
and what is their relation to Fourier analysis? Where do the scaling 
function and the wavelet function come from? Wavelet analysis is based on 
the decomposition of a piecewise constant approximation function into a 
coarser appro-ximation and a detail function. 

We stop for presentation  the concept of multiresolution analysis (MRA) 
which is related to the study of the signals f of different levels of 
resolution, each of them being a finer version of  f.  We will also know the 
function that generates MRA. It is called the father wavelet and it 
satisfies two scale relation or dilation equation. The properties of the 
father wavelet are revealed and one presents three methods for construction 
of this spe-cial function: by iteration, by Fourier analysis, by recursion. 
Examples are delivered and the role of cardinal B-splines are highlighted. 


Further on, we introduce mother wavelet and we indicate possibilities to 
obtain it from a given scale function. This way, one observes that the 
mother wavelet associated with a certain MRA is not unique. On the other 
hand, we provide lots of examples so as to clarify all notions involved. At 
the final part, aspects regarding wavelet decomposi-tions and 
reconstructions are emphasized. 

 


Title: ON APPROXIMATION OF FUNCTIONS BY LINEAR POSITIVE OPERATORS
Date:05/04/2010, 15.30 

 


Abstract of the conference 

Approximation Theory represents an old field of mathematical research with a 
great potential for applications to a wide variety of problems. In the 
fifties, a new breath over it has been brought by a systematic study of the 
linear methods of approximation which are given by sequences of linear 
operators, the essential  ingredient being that of positivity. In this 
respect, our talk represents a journey in the world of positive 
approximation process-es (PAP), meeting mathematicians, historical notes and 
outstanding results. 


We start by presenting the roots of this approach, a result due to 
Popoviciu-Bohman-Korovkin, one of the most powerful criterion to decide if a 
sequence of linear positive operators towards the identity operator with 
respect to the uniform norm. Furter on, in distinct sections we indicate 
classical and modern research directions of this field, quantitative 
evaluations of the error of approximation involving moduli of smoothness and 
K-functionals, a probabilistic approach revealing the connection between a 
random scheme and the construction of  a certain PAP. We will present 
examples of classes of operators which approximate functions acting on 
bounded or unbounded intervals. 


Our talk will bring into light recent results about the statistical 
convergence or the matrix summability method. The advantage of replacing the 
uniform convergence by statistical convergence consists in the fact that the 
last convergence models and improves the technique of signal approximation 
in different functions spaces. The convergence in variation and the 
variation detracting property  will be also examined. 


The last part of our conference is devoted to q-Calculus. During the last 
decade it was intensively used in the construction for different 
generalizations of many classical sequences of linear positive operators. 
Our aim is to give a more complete perspective of these achievements. 

 


Dr. Cenap OZEL
Abant İzzet Baysal Üniversitesi
Fen Edebiyat Fakültesi
Matematik Bölümü
Gölköy Kampusu
14280 BOLU
Telefon: +90 374 2541000/1314
e-posta : cenap at ibu.edu.tr