"Polynomial bases in C[0,1] with optimal growth of degrees"
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
Place: Mathematics Seminar Room, SA-141