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In mathematics, specifically in functional and complex analysis, the disk algebra A is the set of holomorphic functions
that extend to a continuous function on the closure of D. That is,
where H denotes the Banach space of bounded analytic functions on the unit disc D.When endowed with the pointwise addition = ƒ + g, and pointwise multiplication = ƒg, 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,
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