Function Theory in the Unit Ball of Cn

Walter Rudin received his PhD in mathematics from Duke University in North Carolina in 1949. Starting in 1950 he took a Moore instructorship at MIT in Cambridge, Massachusetts where he wrote his first mathematical book. He then went to the University of Rochester in Rochester, New York and finally to the University of Wisconsin in Madison, Wisconsin where he has been a Professor of Mathematics since 1959. He is now an Emeritus Professor there.

• Preliminaries.- The Automorphisms of B.- Integral Representations.- The Invariant Laplacian.- Boundary Behavior of Poisson Integrals.- Boundary Behavior of Cauchy Integrals.- Some Lp-Topics.- Consequences of the Schwarz Lemma.- Measures Related to the Ball Algebra.- Interpolation Sets for the Ball Algebra.- Boundary Behavior of H?-Functions.- Unitarily Invariant Function Spaces.- Moebius-Invariant Function Spaces.- Analytic Varieties.- Proper Holomorphic Maps.- The -Problem.- The Zeros of Nevanlinna Functions.- Tangential Cauchy-Riemann Operators.- Open Problems.

"This book by Rudin was written in a period that a new type of approach to functions of several complex variables emerged ... . a basic textbook that is quite accessible, and its reprint will be enjoyed by many researchers and students in complex analysis." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 18, 2011)