Analysis of Operators on Function Spaces

This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018.The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.

My recollections of Serguei Shimorin.- Localization of zeros in cauchy-de Branges spaces.- Radially weighted Besov spaces and the Pick property.- Interpolation between Hilbert spaces.- A panorama of positivity. I: Dimension free.- Inner functions in reproducing Kernel Spaces.- Spherically quasinermal pairs of commuting operators.- Remarks on the Interplay Between Algebra and PDE.- Which quartic polynomials have a hyperbolic antiderivative?.- Positive integral Kernels for polar Derivatives.- The weak type estimates of two different martingale transforms coincide.- Photographs by Serguei Shimorin.