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- Corona_theorem abstract "In mathematics, the corona theorem is a result about the spectrum of the bounded holomorphic functions on the open unit disc, conjectured by Kakutani (1941) and proved by Lennart Carleson (1962).The commutative Banach algebra and Hardy space H∞ consists of the bounded holomorphic functions on the open unit disc D. Its spectrum S (the closed maximal ideals) contains D as an open subspace because for each z in D there is a maximal ideal consisting of functions f with f(z) = 0.The subspace D cannot make up the entire spectrum S, essentially because the spectrum is a compact space and D is not. The complement of the closure of D in S was called the corona by Newman (1959), and the corona theorem states that the corona is empty, or in other words the open unit disc D is dense in the spectrum. A more elementary formulation is that elements f1,...,fn generate the unit ideal of H∞ if and only if there is some δ>0 such that everywhere in the unit ball.Newman showed that the corona theorem can be reduced to an interpolation problem, which was then proved by Carleson. In 1979 Thomas Wolff gave a simplified (but unpublished) proof of the corona theorem, described in (Koosis 1980) and (Gamelin 1980).Cole later showed that this result cannot be extended to all open Riemann surfaces (Gamelin 1978).As a by-product, of Carleson's work, the Carleson measure was invented which itself is a very useful tool in modern function theory. It remains an open question whether there are versions of the corona theorem for every planar domain or for higher-dimensional domains.".
- Corona_theorem wikiPageExternalLink 10050.
- Corona_theorem wikiPageExternalLink ~ijmath.
- Corona_theorem wikiPageID "4499209".
- Corona_theorem wikiPageRevisionID "545343934".
- Corona_theorem authorlink "Lennart Carleson".
- Corona_theorem first "Lennart".
- Corona_theorem hasPhotoCollection Corona_theorem.
- Corona_theorem last "Carleson".
- Corona_theorem txt "yes".
- Corona_theorem year "1962".
- Corona_theorem subject Category:Banach_algebras.
- Corona_theorem subject Category:Hardy_spaces.
- Corona_theorem subject Category:Theorems_in_complex_analysis.
- Corona_theorem type Abstraction100002137.
- Corona_theorem type Algebra106012726.
- Corona_theorem type Attribute100024264.
- Corona_theorem type BanachAlgebras.
- Corona_theorem type Cognition100023271.
- Corona_theorem type Communication100033020.
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- Corona_theorem type Discipline105996646.
- Corona_theorem type HardySpaces.
- Corona_theorem type KnowledgeDomain105999266.
- Corona_theorem type Mathematics106000644.
- Corona_theorem type Message106598915.
- Corona_theorem type Proposition106750804.
- Corona_theorem type PsychologicalFeature100023100.
- Corona_theorem type PureMathematics106003682.
- Corona_theorem type Science105999797.
- Corona_theorem type Space100028651.
- Corona_theorem type Statement106722453.
- Corona_theorem type Theorem106752293.
- Corona_theorem type TheoremsInComplexAnalysis.
- Corona_theorem comment "In mathematics, the corona theorem is a result about the spectrum of the bounded holomorphic functions on the open unit disc, conjectured by Kakutani (1941) and proved by Lennart Carleson (1962).The commutative Banach algebra and Hardy space H∞ consists of the bounded holomorphic functions on the open unit disc D.".
- Corona_theorem label "Corona theorem".
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- Corona_theorem sameAs Q5172143.
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- Corona_theorem wasDerivedFrom Corona_theorem?oldid=545343934.
- Corona_theorem isPrimaryTopicOf Corona_theorem.