用Hermite-Fejér型插值多项式逼近连续函数

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

关于En(WPr)P的一些结果

Let L_p be the function space consisting of periodic functions f(t)with period 2π and f (t) be p-summable on a period, F_2π-1 be the set of all trigonometric polynomials of degree相似文献   

周期点集为闭集的圆周自映射周期点的周期

Let S¹ denote the circle. In this paper, we show the following.Theorem. Let f: S¹→S¹ be a continuous map and suppose f has a fixed point and the set of periodic points of f is closed, then the period of each periodic point of f is a power of 2.Corollary. Let f: S¹→S¹ be a continuous map and suppose the set of periodic points of f is closed, then there exists an odd integer m such that the set of periods of periodic points of f is contained in the set {m·2ⁿ; n = 0,1,2,…}.     

SL(3,pn)的Cartan不变量

Let G = SL(3,K) be a simply connected, semi-simple algebraic group of type A₂ over an algebraically closed i'ield K of characteristic p>0. Let Γ_n = SL(3,pⁿ) be a finite subgroup consisting of fixed points of the Frobenius morphism F² of G.     

分数阶连续模与Fourier级数的绝对收敛

Let f∈L_2π and let(?) be its Fourier series. For any γ>0 , the continuity modulus of fractional order γ of f∈L_2π^p(p≥1) is defined by.     

平稳弱相关过程积分的收敛性

Lei g(x,ω) be a stationary weakly conelated process, G(t, x) be the Green's function and G(x) be a function with a smooth one-order derivative. Define stochastic processes ξ(t,ω)=∫₀¹G(t,x)g(x,ω)dx (0≤t≤1) and η(t,ω)=∫₀^tG(x)g(x,ω)dx (0≤t≤T) In this paper we give the strong approximations of random variables ξ(t) and η(t) to normal variables, and also give a weakly in variance principle for process η(·).     

球面Schr?dinger算子的迹

Let S be a unit sphere in R³,Δ_θ,φ be the spherical Laplasian and q(θ,φ) be a continuous function on S. The following trace formulae are proved for the eigenvalues μ_n of L₀=-Δ_θ,φ and λ_n of L=L₀+q.     

关于富里埃及数和幂级数的蔡查罗平均

Let f(x) be a periodic function of period 2π,|f(x)|and |f(x)|^p integrable on [0,2π].It is said to be f∈H_X¹,if (∫₀^2π|f(x+h)-f(x)|^pdx)^1/p≤|h|.It is said to be f∈H_X²,if (∫₀^2π|f(x+h)+f(x-h)-2f(x)|^pdx)^1/p≤2|h|.     

A Generalization of Lappan’s Theorem to Higher Dimensional Complex Projective Space

In this paper, the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result: Let f be a holomorphic mapping of ? into Pⁿ(C), and let H₁, · · · , H_q be hyperplanes in general position in Pⁿ(C).Assume that sup {(1 ? |z|²)f^?(z) : z ∈ q[ j=1 f^?1(H_j )o < ∞,if q ≥ 2n² + 3, then f is normal.     

关于Grünwald插值算子及其应用

本文研究了基于Jacobi多项式J_n^(α,β)(x)(0<α,β<1)的零点{x_k}_lⁿ的Grünwald插值多项式G_n(f;x)=(?)f(x_k)l_k²(x),证明了G_n(f;x)在(-1,1)内的任一闭子区间上一致收敛于连续函数f(x);从而拓广了Grünwald所得结果。     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。