The Corona Problem

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. Mathematiciansboth veterans and newcomerswill 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.

Contains a comprehensive treatment of the status of the corona problem Treats both the history and context of the corona problem Features many new results about the corona problem Includes supplementary material: sn.pub/extras

Autorentext
Steven Krantz, Ph.D., is Chairman of the Mathematics Department at Washington University in St. Louis. An award-winning teacher and author, Dr. Krantz has written more than 45 books on mathematics, including Calculus Demystified, another popular title in this series. He lives in St. Louis, Missouri.

Inhalt
The History of the Corona Problem (R.G. Douglas, S.G. Krantz, E.T. Sawyer, S. Treil, B.D. Wick).- Corona Problem for H^\infty on Riemann Surfaces (A. Brudnyi).- Connections of the Corona Problem with Operator Theory and Complex Geometry (R.G. Douglas).- On the Maximal Ideal Space of a Sarason-Type Algebra on the Unit Ball (J. Eschmeier).- A Subalgebra of the Hardy Algebra Relevant in Control Theory and its Algebraic-Analytic Properties (M. Frentz, A. Sasane).- The Corona Problem in Several Complex Variables (S.G. Krantz).- Corona-Type Theorems and Division in Some Function Algebras on Planar Domains (R. Mortini, R. Rupp).- The Ring of Real-Valued Multivariate Polynomials: An Analyst's Perspective (R. Mortini, R. Rupp).- Structure in the Spectra of Some Multiplier Algebras (R. Rochberg).- Corona Solutions Depending Smoothly on Corona Data (S. Treil, B.D. Wick).- On the Taylor Spectrum of M-Tuples of Analytic Toeplitz Operators on the Polydisk (T.T. Trent).