## Seminar:

Fall 2017, Thursdays, Blocker 628, 4:00-4:50 PM
__ Date:__ ** November 9 **

**" Weighted polynomial approximation and related problems in harmonic analysis "**

**Mahishanka Withanachchi**

__Abstract__In 1920s Bernstein asked the question whether we could generalize the Weierstrass approximation theorem for the whole real line which is a classical problem in harmonic analysis called the "Bernstein problem". Since polynomials doesn't decay at infinity we need weighted polynomial approximation and thus it is called the Bernstein problem on weighted polynomial approximation of the real line. Even though several mathematicians worked on this problem and several specific results are available, the general problem is still unsolved. I hope to introduce classical results and the work of my adviser Dr.Alexei Poltoratski ,and several other mathematicians who worked on this problem in 1990s. I'm also planing to introduce the results that I was able to prove and future direction of my research