Sharp Nikolskii inequalities with exponential weights

w _a(x)=exp(–x^a), xR, a0. , N _n (a,p,q) — (2), _n P _nw_ap, CN_n(a,p, q)P_nw_aq. , — , {P _n}, .

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This material is based upon research supported by the National Science Foundation under Grant No. DMS-84-19525, by the United States Information Agency under Senior Research Fulbright Grant No. 85-41612, and by the Hungarian Ministry of Education (first author). The work was started while the second author visited The Ohio State University between 1983 and 1985, and it was completed during the first author's visit to Hungary in 1985.     

Convergence of simultaneous Padé approximants to two dilogarithms

. .     

Exact error bound of approximation by interpolating splines inL-metric on the classesW p r (1≦p

Корнейчук  Н. П. 《Analysis Mathematica》1977,3(2):109-117

О Сходимости Лагранжева Интерполирования В Некоторых Множествах Функций

.      

Converse results on equiconvergence of interpolating polynomials

, n- n- 1 , . , , ( « ») f .     

On strong summability of multiple Fourier series and smoothness properties of functions

_n —n- — ƒ()L _v (T _n ), 1f, - -. -.     

Approximation of functions of several variables by trigonometric polynomials with given number of harmonics,and estimates of ε-entropy

. - . .. . . . , 340 048 . 1      

On a class of orthogonal series

, [0, 1], (n+1) n-. . [2]. — (. 5.4 5.6). . 6.4 2 [5]. , [4]. , , [6] [7]. [1].     

On an inequality of Longnecker and Serfling

— [2], [5], [7], [8], , , . , . , .     

On an application of infinitely divisible distributions to quadrature problems

— - , .     

On the Cesàro summability of orthogonal sequences

(C, ). , . 0<<1. 1) - ( _k ), _k =a _k , (C, ), . 2) , , (C, ) ; _k = =¦a _k ¦.     

On the convergence in a restricted sense of multiple series

Z ^d — k=(k ₁, ...,k _d) k _j,d1.d- (8), . . a _k s _m= a _k s, >0 N, min (m ₁,...,m _d)N, ¦s _m–s¦. , , >0 N, min (m ₁,...,m _d)N min (n ₁,...,n _d)N, ¦s _m–s _n. . , (8) , >0 N, max (b ₁,...,b _d) N, m — Z ^d , m1, ¦s(b, m)¦ where      

Pointwise convergence of multiple Fourier series using different convergence notions

, . , L ^p (²) p>1 . , C(T³), - , . - .

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This work was completed while the first named author was a visiting professor at Indiana University, Bloomington, Indiana; and the second named author was a visiting professor at Ohio State University, Columbus, Ohio, U.S.A.     

Majorization versus power majorization

, . , [1]. 42.     

A Hubert space characterization among function spaces

— [0,1] ,E — - e=1 [0,1]. I — _E =1, E=L ₂ x _e =xL ₂ x E.

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This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund.     

Идеологиыеское знаыение геометрии бояи—лобаыевского

... , , . ( ) , , . (. )     

Замечания о Сходкмости лагранжева интерполрования

( qP. )     

On certain imbedding and extension theorems for a weighted class of functions

n- , S n–1 m (0m<n), () S . () , ().     

Замечания о порядке погрещности интерполяции

.      

On the existence of functions fromL p,p≧1, whose Fourier series converge to zero on a prescribed set and diverge unboundedly outside it

. E, E [–, ], E>0 ( — ) fL ₁ ([–, ]),f=0 [–, ]E, . . E . . . 1955 . ( ) . 1918 . ( ) L , .