共查询到20条相似文献,搜索用时 111 毫秒
1.
记Un(z)是第二类Chebyshev多项式,伴随函数,这里讨论基于的双正交级数和其共轭级数的部分和逼近问题。 相似文献
2.
本文讨论Laplace-Fourier级数(球调和级数)的部分和算子的几乎处处逼近问题,确定了部分和算子在一类Riesz位势空间上逼近的阶. 相似文献
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本文建立了用付氏变换在三角级数求和中的新的重要定理,并用付氏变换的已知结果,解决了不少困难和复杂的三角级数求和问题.这是三角级数求和的新方法,作者曾用以编著了数以万计的三角级数之和的大表.许多结果都是新的. 相似文献
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本文给出Lesendre-Fourier级数和共轭Lesendre-Fourier级数的部分和点态逼近ω-型单调连续函数的速度. 相似文献
7.
本文讨论了牛曼─贝塞尔级数的共轭级数,建立了其部分和与相应的共轭Fourier三角级数的部分和之间的关系,同时给出了两个收敛定理。 相似文献
8.
假设三角级数的系数具有拟单调性,给出了级数按L^1[0,2π]中的范数收敛于其和函数的一个判别条件,推广了文献中的有关结果. 相似文献
9.
本文确定了一类函数的Hausdorff维数,它包含了一大类缺项三角级数.所得结果很自然地引入了一类断片(Fractal)集. 相似文献
10.
Paley,Zygmund和Kahane等人研究过系数是Gauss随机变量序列,Steinhaus序列、Rademacher序列或更一般的独立对称随机变量的随机三角级数的a.s.收敛性、可积性、连续性.Kahane还给出了次Gauss随机三角级数a.s.表示的连续函数的连续模及轨道性质。但至今,对于系数是其它独立对称随机变量的三角级数还没有一般的结果,本文研究系数是指数型随机变量的随机三角级数的连续模、象集和水平集的性质。 相似文献
11.
Zhang Peixuan 《分析论及其应用》1994,10(1):47-57
In this paper, we discuss the relation between the partial sums of Jacobi series on an elliptic region and the corresponding
partial sums of Fourier series. From this we derive a precise approximation formula by the partial sums of Jacobi series on
an elliptic region. 相似文献
12.
The uniform approximation of functions from a certain class on compact sets was performed first by means of polynomials, then by partial sums of universal functional series, and further by special sums associated with functional series. In this paper we construct universal sums associated with Hermite polynomials (any function from this class on compact sets is approximated by these sums). We apply the matrix transformation method that was used earlier for constructing special sums for other functional series. 相似文献
13.
In this paper, for the partial sums with their maximums of a sequence of i.i.d. random variables, we show the precise rates in the general law of the iterated logarithm of a kind of weighted infinite series of the first moment convergence by using the strong approximation and point out the equivalent moment conditions. 相似文献
14.
In this paper we consider the uniform approximation of a function from a certain class by sums obtained as a result of some
matrix transformation of the universal power lacunary series. 相似文献
15.
We define a kind of spectral series to filter off completely the Gibbs phenomenon without overshooting and distortional approximation near a point of discontinuity. The construction of this series is based on the method of adding the Fourier coefficients of a Heaviside function to the given Fourier partial sums. More precisely, we prove the uniform convergence of the proposed series on the class of piecewise smooth functions. Also, we attach two numerical examples which illustrate the uniform convergence of the suggested series in comparison with the Fourier partial sums. 相似文献
16.
M. Freund 《Results in Mathematics》1988,13(1-2):81-98
The rate of best polynomial approximation of an analytic function on a compact Faber set K is characterized in terms of the rate of growth of its Faber coefficients and compared with the rate of approximation by the partial sums of the Faber series. Also the convergence of sequences of interpolating polynomials constructed for various systems of nodes is studied by considering the growth of the interpolated function. Under appropriate assumptions on K the approximation by interpolating polynomials can be incorporated in the characterization theorem. Emphasis is laid on high precision in describing the rate of approximation and on admitting a large class of functions. 相似文献
17.
1IntroductionAwaveletorthonormalbasisoftheusualLebesquesquareintegrablefunctionspaceLZissuchasystem{Vjj,k}i,k,z,with'Wj,k(.)=Zany(Zi'--k)beinggeneratedfromthetranslationsanddyadicdilationsofasillglefunction,rk.It11asbeenshownthatthesystem{ioj,~}j,kezcouldbeservedasSchauderbasisorunconditionalbasisformostfunctionspaces[2].ThepurposeofthispaperistopresentsomepropertiesoftheorthonormalwaveletsystemintheperiodiccauseandtoindicatesimilarityofthissystemtoothersystemssuchasthesysemsofHaarandFI'an… 相似文献
18.
Series in multiplicative systems χ with generalized monotone coefficients are studied. Necessary and sufficient Hardy–Littlewood type conditions for the sums of such series to belong to the Lorentz space are proved. As corollaries, we establish estimates of best approximation in the system χ and Konyushkov-type theorems on the equivalence of O- and ?-relations for the weighted sums of the Fourier coefficients in the system χ and for the best approximations. 相似文献
19.
In this paper, Lorentz space of functions of several variables and Besov's class are considered. We establish an exact approximation order of Besov's class by partial sums of Fourier's series for multiple trigonometric system. 相似文献
20.
L. Leindler 《Analysis Mathematica》2009,35(1):51-60
The aim of the paper is to give a relaxed estimate pertaining to the degree of approximation of the partial sums of Fourier series in a new Banach space of functions introduced by Das, Nath and Ray [2]. Furthermore, applying our new result, we verify, under certain natural conditions, that some classical means have the same approximation degree as the partial sums. 相似文献