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- Disk_algebra abstract "In function theory, the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions f : D → C,where D is the open unit disk in the complex plane C, f extends to a continuous function on the closure of D. That is,where denotes the Banach space of bounded analytic functions on the unit disc D (i.e. a Hardy space).When endowed with the pointwise addition, (f+g)(z)=f(z)+g(z),and pointwise multiplication,(fg)(z)=f(z)g(z),this set becomes an algebra over C, since if ƒ and g belong to the disk algebra then so do ƒ + g and ƒg.Given the uniform norm,by construction it becomes a uniform algebra and a commutative Banach algebra. By construction the disc algebra is a closed subalgebra of the Hardy space H∞. In contrast to the stronger requirement that a continuous extension to the circle exists, it is a lemma of Fatou that a general element of H∞ can be radially extended to the circle almost everywhere.".
- Disk_algebra wikiPageID "761221".
- Disk_algebra wikiPageRevisionID "543805495".
- Disk_algebra hasPhotoCollection Disk_algebra.
- Disk_algebra subject Category:Banach_algebras.
- Disk_algebra subject Category:Complex_analysis.
- Disk_algebra subject Category:Functional_analysis.
- Disk_algebra type Abstraction100002137.
- Disk_algebra type Algebra106012726.
- Disk_algebra type BanachAlgebras.
- Disk_algebra type Cognition100023271.
- Disk_algebra type Content105809192.
- Disk_algebra type Discipline105996646.
- Disk_algebra type KnowledgeDomain105999266.
- Disk_algebra type Mathematics106000644.
- Disk_algebra type PsychologicalFeature100023100.
- Disk_algebra type PureMathematics106003682.
- Disk_algebra type Science105999797.
- Disk_algebra comment "In function theory, the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions f : D → C,where D is the open unit disk in the complex plane C, f extends to a continuous function on the closure of D. That is,where denotes the Banach space of bounded analytic functions on the unit disc D (i.e.".
- Disk_algebra label "Disk algebra".
- Disk_algebra label "Diskalgebra".
- Disk_algebra sameAs Diskalgebra.
- Disk_algebra sameAs m.0395jp.
- Disk_algebra sameAs Q2676720.
- Disk_algebra sameAs Q2676720.
- Disk_algebra sameAs Disk_algebra.
- Disk_algebra wasDerivedFrom Disk_algebra?oldid=543805495.
- Disk_algebra isPrimaryTopicOf Disk_algebra.