On a "Lethargic" Theorem

When

Start: 09/21/2015 - 4:00pm
End : 09/21/2015 - 5:00pm

Category

Applied Math Seminar

Speaker

Asuman Aksoy (Claremont McKenna College)

Abstract

One of the most important theorems used in constructive theory of functions is called Berstein's "lethary" theorem [3]. The theorem states that if $\{d_i\}$ is a sequence of nonnegative numbers with $\lim d_i =0$ then there exists a function $f\in C[0,1]$ such that dist $(f, P_i) = d_i$ for $i=0,1,2,3,\dots$ , where C[0,1] denotes the Banach space of all continuous, real-valued functions defined on the interval $[0,1]$ with supremum norm, and $P_i$ denotes the space of all polynomials of degree $\leq i$ . In this talk, after examining the developments in this theory [1], we present a lethargic theorem for Fr ́echet spaces [2]. This is joint work with G. Lewicki.