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In functional analysis, a weighted space is a space of functions under a ''weighted norm'', which is a finite norm (or semi-norm) that involves multiplication by a particular function referred to as the ''weight''. Weights can be used to expand or reduce a space of considered functions. For example, in the space of functions from a set to under the norm defined by: , functions that have infinity as a limit point are excluded. However, the weighted norm is finite for many more functions, so the associated space contains more functions. Alternatively, the weighted norm is finite for many fewer functions. When the weight is of the form , the weighted space is called ''polynomial-weighted''. ==References== 〔 * 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「Weighted space」の詳細全文を読む スポンサード リンク
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