ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ - ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ
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Σειρά Ομιλιών

TOPICS IN FOURIER ANALYSIS

Prof. Alexander Olevskii
Tel-Aviv University

Σεπτέμβριος 2002

Ο καθηγητής Olevskii επισκέπτεται το Τμήμα Μαθηματικών στη «θέση Πηχωρίδη», από 10 Σεπτεμβρίου 2002, για ένα μήνα. Θα δώσει σειρά ομιλιών με τα ακόλουθα θέματα.

1. Homeomorphisms of the circle and Fourier expansions.
   The following general problem will be discussed: to which extent one can improve fundamental properties of Fourier expansions by an appropriate change of variable. A probabilistic version of the problem will be considered as well.

2. Almost integer translates.
   We will focus on the following phenomenon: for any (nonzero) perturbation of integers , $h(n) = n + o(1)$, there exists a ``generator'', that is a function $f$ in $L^2({\Bbb R})$ such that the family of translates ${\left\{{f(t-h(n)}\right\}}$ spans all the space.

3. Representation of functions by trigonometric series.
   How many frequencies are needed for representation of any function as a sum of the corresponding harmonics? In particular what can be done using the positive frequencies only? These and some related problems will be considered.

In each subject a historical introduction will be given, a survey of some classical results and the recent progress and some open problems will be described.