Integrable Systems and Random Matrix Theory Seminar
An extremal problem for the Bergman kernel of orthogonal polynomials
Monday, October 10, 2022
4:00-5:00 PM
ZOOM ID: 926 6491 9790
Off Campus Location
The notion of optimal measures associated to a compact set K in Euclidean space
is related to that of optimal designs in statistics. This can be reformulated in terms
of an optimization problem related to Bergman functions associated to measures on K.
After a brief motivational discussion, we discuss another optimization problem involving
these Bergman functions which itself is related to finding polynomials of extremal
growth for K at a point outside of K. Using potential theory and estimates for Faber
polynomials, we prove an asymptotic result regarding this problem when K is a planar
compact set bounded a sufficiently regular closed curve. Speaker(s): Norman Levenberg (Indiana University)
is related to that of optimal designs in statistics. This can be reformulated in terms
of an optimization problem related to Bergman functions associated to measures on K.
After a brief motivational discussion, we discuss another optimization problem involving
these Bergman functions which itself is related to finding polynomials of extremal
growth for K at a point outside of K. Using potential theory and estimates for Faber
polynomials, we prove an asymptotic result regarding this problem when K is a planar
compact set bounded a sufficiently regular closed curve. Speaker(s): Norman Levenberg (Indiana University)
| Building: | Off Campus Location |
|---|---|
| Location: | Virtual |
| Event Type: | Workshop / Seminar |
| Tags: | Mathematics |
| Source: | Happening @ Michigan from Department of Mathematics, Integrable Systems and Random Matrix Theory Seminar - Department of Mathematics |
