Walter Rudin (auth.)3540682724, 9783540682721
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
Table of contents :
Front Matter….Pages i-xiii
Preliminaries….Pages 1-22
The Automorphisms of B ….Pages 23-35
Integral Representations….Pages 36-46
The Invariant Laplacian….Pages 47-64
Boundary Behavior of Poisson Integrals….Pages 65-90
Boundary Behavior of Cauchy Integrals….Pages 91-119
Some L p -Topics….Pages 120-160
Consequences of the Schwarz Lemma….Pages 161-184
Measures Related to the Ball Algebra….Pages 185-203
Interpolation Sets for the Ball Algebra….Pages 204-233
Boundary Behavior of H ∞ -Functions….Pages 234-252
Unitarily Invariant Function Spaces….Pages 253-277
Moebius-Invariant Function Spaces….Pages 278-287
Analytic Varieties….Pages 288-299
Proper Holomorphic Maps….Pages 300-329
The $$ bar partial $$ -Problem….Pages 330-363
The Zeros of Nevanlinna Functions….Pages 364-386
Tangential Cauchy-Riemann Operators….Pages 387-402
Open Problems….Pages 403-417
Back Matter….Pages 419-436
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