The Jackson theorem inB a spaces

As everyone knows, the classical Jackson theorem in approximation theory was generalized in L_p spaces by R. A. Devore^[4]. In this paper, we proved the Jackson theorem in B_a spaces which introduced by Ding Xia Xi.     

推广Jackson逼近阶定理

在随机函数的环境下,推广了经典函数逼近论中的Jackson逼近阶定理.建立了随机函数均方连续模的概念,并得到其有关性质后,研究了四种不同条件下随机函数被随机系数三角多项式逼近的阶之估计.     

The multidimensional Jackson theorem in Lp

This article considers the best approximation of a periodic function of several real variables by trigonometric polynomials with hyperbolic-cross harmonics. Theorems are proved on upper bounds for the indicated best approximation in terms of the modulus of continuity of the given function.Translated from Matematicheski Zametki, Vol. 52, No. 1, pp. 105–113, July, 1992.     

JACKSON‘S THEOREM FOR COMPACT GROUPS

In this article we consider the generalized shift operator defined by (Shuf)(g)=∫Gf(tut^-1g)dt on compact group G and by help of this operator we define “Spherical” modulus of continuity.So we prove Stechkin and Jackson type theorems.     

Multidimensional Jackson theorem in the L2 SPACE

Translated from Matematicheskie Zametki, Vol. 49, No. 5, pp. 154–156, May, 1991.     

The Jackson theorem inL 2 for Christenson-Levy systems

Translated from Matematicheskie Zametki, Vol., 53, No. 4, pp. 111–130, April, 1993.     

On a minimax theorem

The aim of this note is to prove the following statement. It gives an extension of the theorem proved by O. Y. Borenshtein and V. S. Shul'man in [1].     

ON A MIN-MAX THEOREM

In this paper we prove a nonvariational form of a rain-max problem in [l] and give its application to a periodical problem.     

On a Kleinecke-Shirokov theorem

Czechoslovak Mathematical Journal - We prove that for normal operators N1, $${N_2} \in {\cal L}({\cal H})$$ , the generalized commutator [N1, N2; X] approaches zero when [N1, N2; [N1, N2; X]] tends...     

On a fixed-point theorem

Institute of Mathematics, Hanoi. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 30, No. 3, pp. 93–94, July–September, 1996.     

On a density theorem

Translated from Matematichskie Zametki, Vol. 51, No. 6, pp. 32–40, June, 1992.     

On a comparison theorem

This paper gives a generalization of the Sturm comparison theorem for differential equations (p): y″ = p(t)y, (q): y″ = q(t)y under the assumption that the function p ? q changes its sign exactly once on [a, b] or ∝_t^bp ? q, ∝_a^tp ? q maintain the sign on [a, b]. The results are used for investigating the distributions of zeros of solutions and the derivative of solutions of (p), (q).     

On a theorem of Karlin

Starting from an old result of S. Karlin, we demonstrate the usefulness of couplings within the theory of random systems with complete connections. We also give a short exposé of some limit results for the state sequences associated to random systems with complete connections.     

On a theorem of Ismagilov

If A and B are bounded selfadjoint operators and AB is trace class, then the absolutely continuous part of A + B is unitarily equivalent to the direct sum of the absolutely continuous parts of A and B.     

On a theorem of Picard

We extend Picard's theorem on the existence of elliptic solutions of the second kind of linear homogeneous -order scalar ordinary differential equations with coefficients being elliptic functions (associated with a common period lattice) to linear homogeneous first-order systems. In particular, the qualitative Floquet-type structure of fundamental systems of solutions in terms of elliptic and exponential functions, polynomials, and Weierstrass zeta functions of the independent variable is determined. Connections with completely integrable systems are mentioned.