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




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