Sharpening of Stečkin's theorem to strong approximation with exponentp

— , B _n , B p1., , p=1 , - . , , , p.     

Transferring estimates for zonal convolution operators

_p - , . Ad- .     

Жизнь и деятельность яноша Бояи

: . BOLYAI.     

On some problems of interpolation by ℒ-splines

_n (D) — ,s — _n (D), _v (v=1, 2, ...,s/2) — . _m={0x ₀<x ₁<...<x _2m–1<2,x _2m =x ₀+2} , x _j +1–x _j <(4s max _v )^–1,j=0, 1, ..., 2m –1, ( ) 2- - _n,m 2m , _m . , L _q - (1q) W ( _n )={f ₂ :f ^(n–1)AC ₂ , _n (D)f 1} 2- - (s _n f), _m . , - - _n,m .

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The author expresses his gratitude to Yu. N. Subbotin for a useful discussion on the results of this paper.     

Discretization with interpolating approximation

.     

On the divergence of spherical sums of double Fourier-Haar series

. : [0, +) [0, +) - , u+ (u) (u)=o(u lnu). [0, 1]² f , ¦f¦ L([0, 1]²), - [0, 1]².     

О предельном распределении для сумм независимых слууайных велиуин на бикомпактных коммутативных топологиуеских группах

,      

Maximal inequalities,convexity inequality,and their duality. II

, , . . . [1], , . , , ., , L logL. , , . . . . [5]. , .     

Замечания об ихтерполировании

.      

О Сходимости метода подобластей

.      

Morera type theorems on the unit disc

, . . : , , , , .     

Mixed-norm estimates for a class of integral operators

(, ) — R ^m ×R ⁿ . f R ^m ×R ⁿ f_p,q, f L _p (R ^m) x y, L^q(Rⁿ). ׃ _q,r cƒ _p,r , ׃ R ^m ×R ⁿ , , , q r . , ( ¦¦) K ₀ (y); p, g r , K ₀.     

Fenchel-type duality for matroid valuations

The weighted matroid intersection problem has recently been extended to the valuated matroid intersection problem: Given a pair of valuated matroidsM _i = (V, _i , _i ) (i = 1,2) defined on a common ground setV, find a common baseB _{1 2} that maximizes ₁ (B) + ₂ (B). This paper develops a Fenchel-type duality theory related to this problem with a view to establishing a convexity framework for nonlinear integer programming. A Fenchel-type min max theorem and a discrete separation theorem are given. Furthermore, the subdifferentials of matroid valuations are investigated. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Part of this paper has been presented at fifth SIAM Conference on Optimization, Victoria, May 1996.This work was done while the author was at Forschungsinstitut für Diskrete Mathematik, Universität Bonn, 1994–1995.     

The trace to subsets ofR n of Besov spaces in the general case

R ⁿ. , , , F R ⁿ, F , R ⁿ R ⁿ . ^p,q (Rⁿ), >0, 1, q, — ( ) Rⁿ. , ^p,q (Rⁿ) ^F Rⁿ. , q B ^p,q (F), = – (n–)/, >0, — « », ad — F, . , . : , F=R ^d,F— « » F— R ⁿ, « », F. .

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This work has been supported in part by the Swedish Natural Science Research Council.     

О лагранжевом интерполировании с узлами в корнях многочленов сонина-маркова

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Decomposing symmetric exchanges in matroid bases

LetB,B be bases of a matroid, withX B, X B. SetsX,X are asymmetric exchange if(B – X) X and(B – X) X are bases. SetsX,X are astrong serial B-exchange if there is a bijectionf: X X, where for any ordering of the elements ofX, sayx _i ,i = 1, , m, bases are formed by the sets B₀ = B, B_i = (B_i–1 – x_i) f(x _i), fori = 1, , m. Any symmetric exchangeX,X can be decomposed by partitioning X = _i=1 ^m Y_i, X = _i=1 ^m Y_i, X, where (1) bases are formed by the setsB ₀ =B, B _i = (B _i–1 –Y _i ) Y _i ; (2) setsY _i ,Y _i are a strong serialB _i–1 -exchange; (3) properties analogous to (1) and (2) hold for baseB and setsY _i ,Y _i .     

On convergence of function series

, a _n f _n (x) . .     

Convergence of simultaneous Padé approximants to two dilogarithms

. .     

Homogenization of Some Elasticity Problems with Rapidly Oscillating Convex Constraints on Displacements

The problem of homogenization is considered for an elastic body occupying a perforated domain = obtained from a fixed domain and an -contraction of a 1-periodic domain .     

On approximation of functions on the half-line by algebraic polynomials

, . , .