...Therefore, if D is bounded and f is continuous including the boundary of D , then the maximum value of | f | must be taken on the boundary of D. (5) Liouville's theorem There are no regular and bounded functions on the complex plane C other than constants. In addition, the following theorem can be derived from (1). ... *Some of the terminology that mentions "Liouville's theorem" is listed below. Source | Heibonsha World Encyclopedia 2nd Edition | Information |
…したがって,Dが有界でfがDの境界も込めて連続ならば|f|の最大値はDの境界でとられなければならない。(5)リウビルの定理Liouville’s theorem 複素平面Cで正則で有界な関数は,定数以外には存在しない。 また,(1)から次の定理が導かれる。… ※「Liouville's theorem」について言及している用語解説の一部を掲載しています。 出典|株式会社平凡社世界大百科事典 第2版について | 情報 |
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