Abstract
The traditional definition of a function algebra is that it is any closed subalgebra of the continuous functions on a compact Hausdorff space. For us—at least at the beginning—the relevant compact Hausdorff space is the circle T. Classically, an important function algebra has been A(D)—the functions continuous on \( \bar D \) and holomorphic on D. [We call A(D) the disk algebra.] Each such function can be identified with its restriction to the circle. And any such restriction has Fourier series with no coefficients of negative index. So this is clearly a subspace. It also follows by inspection that it is a subalgebra, and is closed.
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© 2006 Birkhäuser Boston
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(2006). Wolff’s Proof of the Corona Theorem. In: Krantz, S.G. (eds) Geometric Function Theory. Cornerstones. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4440-7_11
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DOI: https://doi.org/10.1007/0-8176-4440-7_11
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4339-3
Online ISBN: 978-0-8176-4440-6
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