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§1.引言 在多项式保形逼近理论中面临以下两个基本问题: 问题1.对于k≥2,R~k中是否存在k维紧凸集E及C(E)上的保凸正线性算子列L_n:C(E)→P_n满足:?凸函数f∈C(E),||L_nf-f||_E→0(n→∞)? 问题2.对于k≥2以及R~k中的任意k维紧凸集E和任意凸函数f∈C(E),是否存在一列多项式p_n∈P_n,使每一个p_n在E上为凸函数,并且||p_n-f||_E→0(n→∞)? 相似文献
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1.引言 用△_k是表示R~k中的单纯形:△_k={X=(x_1,x_2,…,x_k)∈R~k|x_i≥0,i=1,2,…,k;sum from i=1 to k(x_i)≤1};C(△_k)表示定义在△_k上的连续函数的全体.记||f||=||f||_(△_k):=sup|f(X)|,ω(f,t):=sup |f(X)-f(Y)|。连续函数ω(t),t∈[0,+∞)称为 相似文献
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矩阵非齐次特征值分析 总被引:5,自引:0,他引:5
矩阵非齐次特征值分析卢旭光(清华大学应用数学系)MATRIXINHOMOGENEOUSEIGENVALUEANALYSIS¥LuXu-guang(TsinghuaUniversity)Abstract:Inthispaperwestudythemat... 相似文献
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We establish the concept of shapes of functions by using partial differential inequalites.Our definition about shapes includes some usual shapes such as convex,subharmonic,etc.,andgives many new shapes of functions.The main results show that the shape preserving approxi-mation has close relation to the shape preserving extension.One of our main results shows thatif f∈C(Ω)has some shape defined by our definition,then f can be uniformly approximatedby polynomials P_n ∈p_n(n∈N)which have the same shape in Ω,and the degree of the ap-proximation is Cω(f,n~(-β))with constants C,β>0. 相似文献
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