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Disk algebra

In mathematics, specifically in functional and complex analysis, the disk algebraA(D) (also spelled disc algebra) is the set of holomorphic functionsƒ : D → C{\displaystyle \mathbb {C} }(where D is the open unit disk in the complex planeC{\displaystyle \mathbb {C} }) that extend to a continuous function on the closure of D. That is, A(D)=H∞(D)∩C(D¯),{\displaystyle A(\mathbf {D} )=H^{\infty }(\mathbf {D} )\cap C({\overline {\mathbf {D} }}),}where H(D) denotes the Banach space of bounded analytic functions on the unit disc D (i.e. a Hardy space).

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