|
Mihai Putinar (UC-Santa
Barbara) July 27-28 2015 5E102, Inha University |
Lecture 1. 2:00-3:00 July 27 (Mon), 2015
Poincare variational principle in
potential theory
The talk will translate in modern
language Poincare's famous Acta Mathematica 1897
article, complemented by Torsten Carleman
doctoral dissertation and the work of M. Schiffer on Fredholm eigenvalues of a planar domain.
Lecture
2. 4:00-5:00 July 27 (Mon), 2015
The Friedrichs operator
The Hilbert space angle between Bergman
space and its complex conjugate was studied by Friedrichs
in connection with problems of planar elasticity. I will trace some ideas derived
from Friedrichs influential work, in the context of
modern approximation theory. In particular I will bring into focus Hankel
forms, complex symmetric operators and spectral analysis in a vector space
endowed with two norms.
Lecture
3. 1:00-2:00 July 28 (Tues), 2015
The ellipse revisited
Among all planar algebraic curves the
ellipse is distinguished by carrying Bergman space orthogonal polynomials
enjoying a three term relation. And secondly by not possessing a Riesz-Fejer type decomposition for positive polynomials,
but still enjoying a special sub-normal quantization. Other aspects of modern
mathematical physics, such as Laplacian Growth phenomena, single out the
ellipse.