Disk algebra
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In function theory, the disk algebra (also spelled disc algebra) is the set of continuous functions
- f : D → C,
where D is the closed unit disk in the complex plane C, such that the restriction of f to the interior of D is an analytic function.
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 f and g belong to the disk algebra then so do f+g and fg.
Given the uniform norm ,||f|| = max{| f(z)| :z
D} it becomes a uniform algebra and in particular a Banach algebra.
It is a subalgebra of the Hardy space H∞.
