Georgios Tsikalas
Vanderbilt University
Title
Pick interpolation in the 21st century
Abstract
Suppose that you are given n initial points and n target points in the unit disk of the complex plane. Does there exist a holomorphic self-map of the disk that maps the i-th initial point to the i-th target point for all i? Pick answered this question in 1916: an interpolating function exists if and only if a certain matrix defined in terms of the initial and target data is positive semi-definite.
A search of MathSciNet reveals that in the last decade alone, hundreds of papers
have been written on Pick interpolation. Why so much interest in a problem that was
completely solved that long ago? In this talk, I will discuss the modern approach to Pick interpolation, which connects to various problems in engineering. I will highlight extensions of this approach to interpolation problems in general reproducing kernel Hilbert spaces.