Douglas R.G., Krantz S.G., Sawyer E.T., Treil S., Wick B.D. (eds.) The Corona Problem: Connections Between Operator Theory, Function Theory, and Geometry

New York: Springer, 2014. — 235 p.The purpose of the corona workshop was to consider the corona problem in both one and several complex variables, both in the context of function theory and harmonic analysis as well as the context of operator theory and functional analysis. It was held in June 2012 at the Fields Institute in Toronto, and attended by about fifty mathematicians. This volume validates and commemorates the workshop, and records some of the ideas that were developed within.
The corona problem dates back to 1941. It has exerted a powerful influence over mathematical analysis for nearly 75 years. There is material to help bring people up to speed in the latest ideas of the subject, as well as historical material to provide background. Particularly noteworthy is a history of the corona problem, authored by the five organizers, that provides a unique glimpse at how the problem and its many different solutions have developed.
There has never been a meeting of this kind, and there has never been a volume of this kind. Mathematicians—both veterans and newcomers—will benefit from reading this book. This volume makes a unique contribution to the analysis literature and will be a valuable part of the canon for many years to come.A History of the Corona Problem
Corona Problem for H ∞ on Riemann Surfaces
Connections of the Corona Problem with Operator Theory and Complex Geometry
On the Maximal Ideal Space of a Sarason-Type Algebra on the Unit Ball
A Subalgebra of the Hardy Algebra Relevant in Control Theory and Its Algebraic-Analytic Properties
The Corona Problem in Several Complex Variables
Corona-Type Theorems and Division in Some Function Algebras on Planar Domains
The Ring of Real-Valued Multivariate Polynomials: An Analyst’s Perspective
Structure in the Spectra of Some Multiplier Algebras
Corona Solutions Depending Smoothly on Corona Data
On the Taylor Spectrum of M -Tuples of Analytic Toeplitz Operators on the Polydisk