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In functional and complex analysis, 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, : 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Disk algebra」の詳細全文を読む スポンサード リンク
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