Disk algebra
In mathematics, specifically in functional and complex analysis, the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions ƒ : D → C {\displaystyle \mathbb {C} } (where D is the open unit disk in the complex plane C {\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).