"Polynomial bases in C[0,1] with optimal growth of degrees"

By

**Alexander Goncharov**

Abstract: A polynomial Schauder basis (P_n) in a function space is
called strict if deg P_n=n for all n. Due to the classical result
of Faber, the space C[0,1] does not possess a such basis. On the other hand,
by the Krein-Milman-Rutman theorem, there are polynomial bases in
C[0,1]. The question arises naturally about the optimal growth of degrees
for polynomial bases. This problem was solved by Al.A.Privalov in 1987 and
1991. We give a review of results in this direction and state some open
problems related to the subject.

Tea and cookies will be served before the
seminar.

**Date: ****Thursday, March 11, 2010**

**Time: ****14.40**

**Place: ****Mathematics Seminar Room,
SA-141**