寬度
正文
刻畫巴拿赫空間內對稱點集的“寬狹”程度的一個數量表征。作為逼近論的一個基本概念是蘇聯數學家Α.Η.柯爾莫哥洛夫在1935年首先提出來的。它的基本思想可以從下面的幾何問題提煉出來。在歐氏平面R 2上給出點集
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一般地說,若M是巴拿赫空間X內的關於O點的對稱集,
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在逼近論中對寬度的研究,主要包括兩個方面的問題,即給出dn(M;X)的數量估計,和找出所有能使寬度實現的n 維線性子空間。這些問題的研究不但具有理論意義,而且也具有實際價值。因為這樣會引導找到M的新的、更好的逼近方法。
Α.Η.柯爾莫哥洛夫在1935年研究了X=l2(平方可和的函式空間)內某些函式類的寬度。對寬度理論的系統研究是從50年代由基哈米洛夫開始的,近20年來這一方面的研究取得了很大進展。