## 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 is a sequence of nonnegative numbers with then there exists a function such that dist for , where C[0,1] denotes the Banach space of all continuous, real-valued functions defined on the interval with supremum norm, and denotes the space of all polynomials of degree . 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.

References

[1] J. Almira and A. G. Aksoy On Shapiro’s Lethargy Theorem and Some Appli- cations, Jean. J. Approx. 6(1), 87 − 116, 2014.

[2] A. G. Aksoy and G. Lewicki Bernstein’s Lethargy Theorem in Fr ́echet spaces, arXiv:1503.06190.

[3] S. N. Bernstein, Collected Works, II Moskow,: Akad Nauk SSR. 1954.

Where
Emmy Noether Room, Millikan 1021, Pomona College