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Bounded analytic functions
Mathematical analysis --- Analytic functions. --- Functional analysis. --- Functional analysis --- Analytic functions --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's --- 517.53 --- 517.53 Functions of a complex variable --- Functions of a complex variable
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Approximation theory --- Analytic functions --- Set functions --- 517.5 --- Functions, Set --- Functions of real variables --- Set theory --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's --- Theory of functions --- Analytic functions. --- Approximation theory. --- Set functions. --- 517.5 Theory of functions --- Fonctions d'une variable complexe --- Theorie de la mesure --- Approximation dans le domaine complexe --- Capacites
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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
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During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a careful survey of these results and an introduction to the branch of analysis which contains them. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff and others, appear here in paperback for the first time. The book is accessible to students who have completed standard graduate courses in real and complex analysis. The first four chapters provide the needed background material on univalent functions, potential theory, and extremal length, and each chapter has many exercises to further inform and teach the readers.
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