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具有Gauss测度的Sobolev空间上的函数逼近 总被引:1,自引:0,他引:1
本文讨论了具有Gauss测度的Sobolev空间上的一元周期函数被三角多项式子空间的最佳逼近及被Fourier部分和算子,Vallée—Poussin算子,Ceshxo算子,Abel算子和Jackson算子的逼近,得到了平均误差估计.证明了在平均框架下,在Lq(1≤q〈∞)空间尺度下三角多项式子空间是渐进最优的子空间,但是在L∞空间尺度下,三角多项式子空间不是渐进最优的子空间.还证明了,Fourier部分和算子和Vallée-Poussin算子在Lq(1≤q≤∞)空间尺度下是渐进最优的线性算子.注意到在平均框架以及Lq(1≤q〈∞)空间尺度下,渐进最优的线性算子,如Fourier部分和算子及Vallée—Poussin算子,与最优的非线性算子的逼近效果一样好. 相似文献
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The paper is related to the error analysis of Multicategory Support Vector Machine (MSVM) classifiers based on reproducing kernel Hilbert spaces. We choose the polynomial kernel as Mercer kernel and give the error estimate with De La Vallée Poussin means. We also introduce the standard estimation of sample error, and derive the explicit learning rate. 相似文献
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研究球面神经网络的构造与逼近问题.利用球面广义的de la Vallee Poussin平均、球面求积公式及改进的单变量Cardaliaguet-Euvrard神经网络算子,构造具logistic激活函数的单隐层前向网络,并给出了Jackson型误差估计. 相似文献
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本文研究了单位球上的Qp空间中的de la Vallée Poussin平均算子,并通过高阶光滑模来建立Jackson逼近定理.此外,我们还得到了Bernstein不等式,K-泛函和光滑模的等价刻画等结果. 相似文献
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通过将Vallée-Poussin算子逼近连续函数的能力转化为对辅助数列{g(n)}的上确界的计算,首先利用数列单调有界定理证明辅助数列极限的存在性,之后借助夹逼准则求得辅助数列{g(n)}的极限,即数列{g(n)}的上确界,进而得到Vallée-Poussin算子逼近连续函数的最优估计常数. 相似文献
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借助于球调和多项式的de la Vallée Poussin和构造出了单位球面S^q上一类带形平移网络算子,并给出了其对L^p(S^q)中函数一致逼近的收敛速度.
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Nitin Nitsure 《Proceedings Mathematical Sciences》2002,112(4):539-542
We prove a necessary and sufficient condition for the automorphisms of a coherent sheaf to be representable by a group scheme. 相似文献
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Xiaoping Xu 《代数通讯》2013,41(9):3589-3635
We find a new representation of the simple Lie algebra of type E 7 on the polynomial algebra in 27 variables. Using this representation and Shen's idea of mixed product, we construct a new functor from E 6-Mod to E 7-Mod. A condition for the functor to map a finite-dimensional irreducible E 6-module to an infinite-dimensional irreducible E 7-module is obtained. Our general framework also gives a direct polynomial extension from irreducible E 6-modules to irreducible E 7-modules, which can be used to derive Gel'fand–Zetlin bases for E 7 from those for E 6 that can be obtained from those for D 5 according to our earlier work. 相似文献
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A geometric property is introduced, and it is proved that Banachspaces with this property must carry weakly amenable algebrasof approximable operators. These results are also applied toparticular examples of Banach spaces, including the James spacesand the Tsirelson space. 相似文献
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《Annals of Pure and Applied Logic》2001,107(1-3):193-226
In this article we establish the existence of a number of new orbits in the automorphism group of the computably enumerable sets. The degree theoretical aspects of these orbits also are examined. 相似文献
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E. A. Palyutin 《Algebra and Logic》2003,42(2):112-120
S. Shelah proved that stability of a theory is equivalent to definability of every complete type of that theory. T. Mustafin introduced the concept of being T
*-stable, generalizing the notion of being stable. However, T
*-stability does not necessitate definability of types. The key result of the present article is proving the definability of types for E
*-stable theories. This concept differs from that of being T
*-stable by adding the condition of being continuous. As a consequence we arrive at the definability of types over any P-sets in P-stable theories, which previously was established by T. Nurmagambetov and B. Poizat for types over P-models. 相似文献