Location: SMLC-118 and Zoom
https://unm.zoom.us/j/96832154356?pwd=S3BpaDd1TkNCQmN2L3lZdmVDUXdzUT09
Meeting ID: 968 3215 4356
Passcode: 31415926

Speaker: Robert Dukes

Title: Minimal Error Functions on Irregular Subsets of the Real Line

Abstract: One of the most practical questions in mathematics is how to approximate a complicated function.  The most common approximants are polynomials, since they are simple to evaluate and to apply the techniques of Calculus.  A related problem is to find polynomials that minimize norms over a compact domain, subject to some constraint.  In this talk, we will use Green's Functions to determine upper and lower bounds for both the Chebyshev Polynomials and the Residual Polynomials on subsets of the real line.  In particular, we will show new bounds when the domain is irregular, defined as a set E whose Green's Function takes non-zero values on some part of E.  We will also introduce the concept of semi-regularity, and discuss its necessity for the bounds to apply in certain cases.