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Function Theory in the Unit Ball of ℂ n [electronic resource] / by Walter Rudin.

By: Rudin, Walter [author.].
Contributor(s): SpringerLink (Online service).
Material type: TextTextSeries: Classics in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008Description: XIII, 436 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540682769.Subject(s): Global analysis (Mathematics) | AnalysisAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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.

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