ANALYSIS
SEMINAR

"Kolmogorov's entropy for compact
sets of analytic and smooth functions"

By

Alexander Goncharov

(Bilkent University)

Abstract: Kolmogorov’s
"¡entropy H"(K) of a compact set K in a metric space X is defined as the binary logarithm of the number of
elements in the most economical covering of K by sets with diameters not
more than 2". To possess information about the asymptotics of
the "¡entropy is important in numerical analysis, where basic characteristics of
numerical algorithms typically depend on H"(K). Kolmogorov, Vitushkin,
Babenko, and Erokhin analyzed the asymptotic behavior of the "¡entropy for model compact sets
in the space of analytic functions. Recently Belykh obtained some
generalizations to the case of smooth (maybe non-analytic) functions. A short
review of these results is presented.

Tea and cookies will be served before the
seminar.

Date:
Tuesday, October 25, 2011

Time: 15.40 – 16:30

Place: Mathematics Seminar Room,
SA-141