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71.
研究了球型平移网络对周期函数的逼近问题.文章首先将基函数eimx分别表示成为两种球型平移网络.进一步,将有关多重Fourier级数的Bochner-Riesz平均表示成为球型平移网络的形式.在此基础上构造出了两类球型平移网络序列,并借助于有关Bochner-Riesz平均对Lp空间中函数的逼近结果给出了这两类球型平移网络序列在Lp空间中的逼近阶. 相似文献
72.
Current methods for interpolation and approximation within a native space rely heavily on the strict positive-definiteness of the underlying kernels. If the domains of approximation are the unit spheres in euclidean spaces, then zonal kernels (kernels that are invariant under the orthogonal group action) are strongly favored. In the implementation of these methods to handle real world problems, however, some or all of the symmetries and positive-definiteness may be lost in digitalization due to small random errors that occur unpredictably during various stages of the execution. Perturbation analysis is therefore needed to address the stability problem encountered. In this paper we study two kinds of perturbations of positive-definite kernels: small random perturbations and perturbations by Dunkl's intertwining operators [C. Dunkl, Y. Xu, Orthogonal polynomials of several variables, Encyclopedia of Mathematics and Its Applications, vol. 81, Cambridge University Press, Cambridge, 2001]. We show that with some reasonable assumptions, a small random perturbation of a strictly positive-definite kernel can still provide vehicles for interpolation and enjoy the same error estimates. We examine the actions of the Dunkl intertwining operators on zonal (strictly) positive-definite kernels on spheres. We show that the resulted kernels are (strictly) positive-definite on spheres of lower dimensions. 相似文献
73.
A functional analysis of NOx levels: location and scale estimation and outlier detection 总被引:1,自引:0,他引:1
Manuel Febrero Pedro Galeano Wenceslao González-Manteiga 《Computational Statistics》2007,22(3):411-427
This paper analyzes the NOx levels measured by a control station near a power plant by using techniques for functional data.
First, we test for differences between the levels on working and non working days. Second, we obtain several location estimators
and confidence sets of the center of the functional distribution. Third, we provide scale estimators and confidence sets of
the dispersion of the functional distribution. Finally, a distance based procedure provides a criterion to determinate the
presence of outlying observations, which allows to detect relevant NOx levels. 相似文献
74.
Alexander Dvorsky 《Journal of Functional Analysis》2003,201(2):430-456
In this paper we construct a family of small unitary representations for real semisimple Lie groups associated with Jordan algebras. These representations are realized on L2-spaces of certain orbits in the Jordan algebra. The representations are spherical and one of our key results is a precise L2-estimate for the Fourier transform of the spherical vector. We also consider the tensor products of these representations and describe their decomposition. 相似文献
75.
Shuichi Sato 《Journal of Mathematical Analysis and Applications》2003,278(2):308-323
We prove some weighted estimates for certain Littlewood-Paley operators on the weighted Hardy spaces Hwp (0<p?1) and on the weighted Lp spaces. We also prove some weighted estimates for the Bochner-Riesz operators and the spherical means. 相似文献
76.
本文采用跨音速中性气体屏蔽模型,得到了氢同位素球形靶丸在其相应高能离子轰击下的消融率G_(is)及其定标律,s可为氢或氘。计算表明,当离子与电子的未扰态能量E_(0s)/E_(0e)~2≥1.5时,G_(is)/G_(es)≥20%,G_(es)为靶丸在等离子体电子轰击下的消融率。因此,当聚变实验有中性粒子束注入加热时,需考虑高能离子轰击对靶丸消融的影响。这也为此情况下靶丸消融强化提供了一种解释。 相似文献
77.
We discuss three methods to correct spherical aberration for a point to point imaging system. First, results obtained using
Fermat’s principle and the ray tracing method are described briefly. Next, we obtain solutions using Lie algebraic techniques.
Even though one cannot always obtain analytical results using this method, it is often more powerful than the first method.
The result obtained with this approach is compared and found to agree with the exact result of the first method. 相似文献
78.
Regularity properties of Laguerre means are studied in terms of certain Sobolev spaces defined using Laguerre functions. As
an application we prove a localization theorem for Laguerre expansions. 相似文献
79.
M. A. Pinsky 《Applied Mathematics and Optimization》1994,30(2):171-174
By working with suitable test functions, we obtain an upper bound for the principal eigenvalue of a geodesic ball on a sphere of arbitrary dimension. This bound is sharp in the limiting case when the radius of the ball approaches the diameter of the sphere.This research was supported by ARO Grant 28905-MA. 相似文献
80.
Fourier-Laplace级数的强逼近 总被引:1,自引:0,他引:1
设f是Rn(n≥3)中单位球面∑n-1上的可积函数,Sθ(f)是步长为θ∈R的平移算子.σδN(f)是Fourier-Laplace级数的δ阶Ceaaro平均.如果∫π0
|Sθ(f)-f|p/θ2dθ∈ L∞ (∑n- 1 ),则∑∞k=0 |σλk(f)-f|p∈L∞(∑n-1)且∑∞k=0(f)-f|p∈L∞(∑n-1
),其中Eλk(f)为Cesaro平均σλk的等收敛算子. 相似文献