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
1 online resource (XVIII, 436 pages) : online resource
9783540682769, 9783540682721, 3540682767, 3540682724
915731691
Printed edition:
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