Titlebook: Bounded Analytic Functions; John B. Garnett Textbook 2007 Springer-Verlag New York 2007 algebra.analytic function.function.proof

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Some Extremal Problems,We begin with the basic duality relation

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Some Uniform Algebra,This chapter develops the background from uniform algebra theory which will be needed for our analysis of H∞ below. Our treatment is quite brief. For a complete picture of the general theory the reader is referred to the books of Browder [1969], Gamelin [1969], and Stout [1971].

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Bounded Mean Oscillation,The space BMO of functions of bounded mean oscillation is the real dual space of the real Banach space .. As a complex Banach space, . has dual ./., and so BMO has a close connection to ..

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Interpolating Sequences,A sequence {.} in the disc or upper half plane is an . if every interpolation problem

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Interpolating Sequences and Maximal Ideals,We return to interpolating sequences and their Blaschke products, and in particular to the surprising part they play in unraveling the maximal ideal space of .. In this chapter three topics are discussed.

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Bounded Analytic Functions978-0-387-49763-1Series ISSN 0072-5285 Series E-ISSN 2197-5612

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John B. GarnettCovers a wide range of beautiful topics in analysis.Well-organized with detailed proofs.Contains numerous exercises and motivation