Holon Institute of Technology
 
Dear Colleagues,
 
Our next Colloquium in Mathematics and Computer Science will take
place on Tuesday,  December 18, at 12:00.
 
Speaker: Prof. Yosef Yomdin
 
Affiliation: Weizmann Institute, Rehovot, Israel
 
Title: Fourier Reconstruction of Piecewise-Smooth Functions with
"Smooth" Accuracy
 
Date: Tuesday, December 18, 2012
 
Time: 12:00
 
Venue: Room 424/8, Science Building
 
Abstract:
 
A periodic $C^d$ smooth function $f$ can be reconstructed from its
first $N$ Fourier coefficients with an error of order $1\N^d$.
However, for $f$ only piecewise $C^d$ smooth the classical Fourier
approximation has an error of order $1\N$, no matter how large $d$
is. There is a long standing open problem (Eckhoff
Conjecture) concerning a possibility to gain the "smooth" accuracy
rate $1\N^d$ via a non-linear manipulations with the first $N$
Fourier coefficients of any piecewise $C^d$ smooth function $f$.
 
I plan to discuss this conjecture from various points of view. This
includes a recent progress in Eckhoff Conjecture obtained via
"Algebraic Sampling" approach, and a general bound on sampling
accuracy provided by a combination of Kolmogorov's entropy and
Johnson-Lindenstrauss dimensionality reduction.
 
Joint work with D. Batenkov.
 
Light refreshments will be served at 11:45 am. Everybody is welcome.
 
Looking forward to seeing you all,
 
                 Anatoly Golberg, Dmitry Goldstein, Eugen Mandrescu
 
Holon Institute of Technology, 52 Golomb St, Holon, 03-5026560,
 <http://www.hit.ac.il/acc/golberga/Events/Colloquia.html>
 
---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Anatoly Golberg   <golberga@hit.ac.il>