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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Blaschke product ： ウィキペディア英語版 Blaschke product In complex analysis, the Blaschke product is a bounded analytic function in the open unit disc constructed to have zeros at a (finite or infinite) sequence of prescribed complex numbers :''a''0, ''a''1, ... inside the unit disc. Blaschke products were introduced by . They are related to Hardy spaces. ==Definition== A sequence of points $(a\_n)$ inside the unit disk is said to satisfy the Blaschke condition when : Given a sequence obeying the Blaschke condition, the Blaschke product is defined as :$B(z)=\backslash prod\_n\; B(a\_n,z)$ with factors :$B(a,z)=\backslash frac\backslash ;\backslash frac$ provided ''a'' ≠ 0. Here $\backslash overline$ is the complex conjugate of ''a''. When ''a'' = 0 take ''B''(''0'',''z'') = ''z''. The Blaschke product ''B''(''z'') defines a function analytic in the open unit disc, and zero exactly at the ''a''''n'' (with multiplicity counted): furthermore it is in the Hardy class $H^\backslash infty$.〔Conway (1996) 274〕 The sequence of ''a''''n'' satisfying the convergence criterion above is sometimes called a Blaschke sequence. 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「Blaschke product」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.