Lecturer: Javad Mashreghi

Title: Reproducing Kernel Hilbert Space of Analytic Functions

Abstract: RKHS is a fast-growing topic with numerous connections to other areas of mathematics, as well as profound applications in other basic sciences and engineering. This theory plays a decisive role in complex analysis, statistics, probability, functional analysis and integral operator theory, matrix theory, group representations, machine learning, signal processing and telecommunication, etc. In this course, the emphasize is on the abstract theory of RKHS with a glance to analytic function spaces such as Hardy, Dirichlet, Bergman, model and de Branges-Rovnyak spaces as special cases. 

References:

-V. Paulsen, M. Raghupathi, An Introduction to the Theory of Reproducing Kernel Hilbert Spaces, Cambridge Studies in Advanced Mathematics 152, Cambridge University Press, 2016.

-J. Agler, J. McCarthy, Pick Interpolation and Hilbert function spaces, Graduate Studies in Mathematics 44, American Mathematical Society, 2002.

-J. Mashreghi, Representation Theorems in Hardy Spaces, London Mathematical Society Student Texts (74), Cambridge University Press, 2013.