Bounded Analytic Functions [electronic resource] / by John B. Garnett.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Graduate Texts in Mathematics: 236Publisher: New York, NY : Springer New York, 2007Description: XIV, 463 p. 31 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387497631Subject(s): Mathematics | Functional analysis | Functions of complex variables | Mathematics | Functions of a Complex Variable | Functional AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 515.9 LOC classification: QA331-355Online resources: Click here to access online
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Preliminaries -- Hp Spaces -- Conjugate Functions -- Some Extremal Problems -- Some Uniform Algebra -- Bounded Mean Oscillation -- Interpolating Sequences -- The Corona Construction -- Douglas Algebras -- Interpolating Sequences and Maximal Ideals.
The book, which covers a wide range of beautiful topics in analysis, is extremely well organized and well written, with elegant, detailed proofs. The book has educated a whole generation of mathematicians with backgrounds in complex analysis and function algebras. It has had a great impact on the early careers of many leading analysts and has been widely adopted as a textbook for graduate courses and learning seminars in both the US and abroad. - From the Citation for the 2003 Leroy P. Steele Prize for Exposition The author has not attempted to produce a compendium. Rather, he has selected a range of topics in a many-faceted theory and, within that range, penetrated to considerable depth...the author has succeeded in bringing out the beauty of a theory which, despite its relatively advanced age---now approaching 80 years---continues to surprise and to delight its practitioners. The author has left his mark on the subject. - Donald Sarason, Mathematical Reviews Garnett's Bounded Analytic Functions is to function theory as Zygmund's Trigonometric Series is to Fourier analysis. Bounded Analytic Functions is widely regarded as a classic textbook used around the world to educate today's practioners in the field, and is the primary source for the experts. It is beautifully written, but intentionally cannot be read as a novel. Rather it gives just the right level of detail so that the motivated student develops the requisite skills of the trade in the process of discovering the beauty of the combination of real, complex and functional analysis. - Donald E. Marshall, University of Washington.