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1.
Let f(x)∈C[-1,1],Tn(x)=cos (n arccos x),Un(x)=(sin((n+1)arccosx))/(1-x2)1/2,Pn(x) be the Legendre polynomials of degree n. And let ω(t ) be a given modulus of continuity, Hω={f|ω(f,t)≤ω(t)}.A. K. Sharma and J. Tzimbalario(J. Appro. Th., 13(1975), 431-442) considered the operators Ln,p (f, x) (p= 0, 1, 2,3) and obtained some theorems.In this paper, we prove the following theorems.  相似文献   

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袁小平 《中国科学A辑》1998,41(4):303-311
证明了下列Duffing型方程的所有解的有界性 :d2x / dt2 +x2n+12nj=0 xjpj(t) =0 ,n≥1,其中,p1,p2 ,… ,p2n是 1周期的有Lipschitz连续性的函数,pn+1,… ,p2n是Zygmund连续的 .这表明Duffing型方程的解的有界性不必要求pj(t)的光滑性.  相似文献   

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本文讨论了n为奇数时πn(x)=(1-x2)P′n-1(x)零点上的(0,1,3)插值的正则性及收敛性,其中Pn-1表示n-1次Legendre多项式.  相似文献   

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本文利用尺度‖·‖H(p,∞)研究了一般紧Lie群上Hp函数的临界阶Bochner-Riesz平均算子σRδ:f→σRδf的有界性,得到了如下结果:σRδ是(Hp,H(p,∞))型的,并且‖σRδf‖H(p,∞)≤C‖f‖Hp  相似文献   

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本文求出用Jackson算子Jn(f;x)逼近C2n中的函数f(x)时的准确逼近常数:对?n≥1,有|Jn(f;x)-f(x)|≤(4-6/π)ω(f;1/n)及用阶数不超过n的三角多项式对函数f(x)的最佳逼近常数的上界估计:?n≤1,有Kn(f)e≤(7-(21)/(2π))ω(f;1/n)  相似文献   

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多元Szász—Mirkjan算子的一致逼近   总被引:2,自引:0,他引:2  
本文研究了多元Szása—Mirakjan算子在C2B(T)中的逼近性质,利用K—泛函,建立了等价的逼近定理.主要结果如下 定理设f∈C2B(T),0a) ;(ii)‖Sn,m(f)-f‖=0(n-a);(iii)a)‖f(x+tφ(x),y)-2f(x,y)+f(x-tφ(x),y)‖=0(t<  相似文献   

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Let Mn+p-1 denote the class of functions f(z) = 1/zp+a0/zp-2+a1/zp-2+…+an+p-1zn+…, regular and p-valent in the annulus 0<|z|<1 and satisfying Re((Dn+p f(z))/(Dn+p-1 f(z)))-2)<-(n+p-1)/(n+p),|z|<1,n>-p where Dn+p-1 f(z)=1/zp((zn+2p-1f(z))/(n+p-1)!)(n+p-1).Mn+p?Mn+p-1 is proved. Since M0 is the subclass of p-valent meromorphically starlike functions, all functions in Mn + p-1 are p-valent meromorphically star-like functions. Further the integrals of functions in Mn+p-1, are considered.  相似文献   

8.
王军  王毅 《中国科学A辑》2000,30(3):232-240
设n和k是任意正整数 ,p是素数 ,L(kn) (p)是交换p 群 (Z/pkZ)n 的子群格 ,则存在正整数N(n ,k) ,使得当p >N(n ,k)时 ,L(kn) (p)具有强Sperner性质 .  相似文献   

9.
定光桂 《中国科学A辑》2000,30(8):673-679
证明如果T是L1,A,μ)到L2,B,ν)内的同构且满足‖T‖·‖T -1‖≤1+ε, ε∈(0,1/5),则在一定条件下‖T/T‖接近于一个等距,其误差小于6ε.  相似文献   

10.
关于多元函数最佳逼近精确阶的Timan问题   总被引:1,自引:0,他引:1       下载免费PDF全文
关于找一个充分必要条件使Ωk(f,1/σ)Lp(Rn)=O(Aσ(f)Lp(Rn)),σ→∞,成立的Timan问题被解决.这个条件是Qk(f,δ)Lp(Rn)=O(Ωk+1(f,δ)Lp(Rn)),δ→0.  相似文献   

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We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

13.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

14.
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.  相似文献   

15.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

16.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

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<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.  相似文献   

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