Function Theory in the Unit Ball of Cn

Function Theory in the Unit Ball of Cn. From the reviews: "...The book is easy on the reader. The prerequisites are minimal-just the standard graduate introduction to real analysis, complex analysis (one variable), and functional analysis. This presentation is unhurried and the author does most of the work. ...certainly a valuable reference book, and (even though there are no exercises) could be used as a text in advanced courses." R. Rochberg in Bulletin of the London Mathematical Society. "...an excellent introduction to one of the most active research fields of complex analysis. ...As the author emphasizes, the principal ideas can be presented clearly and explicitly in the ball, specific theorems can be quickly proved. ...Mathematics lives in the book: main ideas of theorems and proofs, essential features of the subjects, lines of further developments, problems and conjectures are continually underlined. ...Numerous examples throw light on the results as well as on the difficulties." C. Andreian Cazacu in Zentralblatt für Mathematik

Autorentext

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.

Zusammenfassung

Function Theory in the Unit Ball of Cn. From the reviews: "The book is easy on the reader. The prerequisites are minimaljust the standard graduate introduction to real analysis, complex analysis (one variable), and functional analysis. This presentation is unhurried and the author does most of the work. certainly a valuable reference book, and (even though there are no exercises) could be used as a text in advanced courses." R. Rochberg in Bulletin of the London Mathematical Society. "an excellent introduction to one of the most active research fields of complex analysis. As the author emphasizes, the principal ideas can be presented clearly and explicitly in the ball, specific theorems can be quickly proved. Mathematics lives in the book: main ideas of theorems and proofs, essential features of the subjects, lines of further developments, problems and conjectures are continually underlined. Numerous examples throw light on the results as well as on the difficulties." C. Andreian Cazacu in Zentralblatt für Mathematik

Inhalt
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.