О Сходимости Тригонометричецкого и Гармонического интерполирования

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Additive functions

1<q<2 L:= _n=1 1/q ⁿ=1/q–1. [0,1] _n()=1, A _n:= _i=1 ^n–1 _i(x)/q^i+1/n x _n(x)=0, _n>. , = _{n=1 n}(x)/qⁿ. F: [0,L]R , F(x)= _{n=1 n}(x)a_n, _n=1 ¦a _n¦<. [0,L]. q(1,2), . , q(1, 2), . .     

On rearrangements of the Haar system in the space BMO

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О Сходимости Лагранжева Интерполирования В Некоторых Множествах Функций

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Onp-Helson sets in R n

p- . E R ⁿ -, f () _p(R ⁿ)., ER ⁿ 2nq ₀, E— - q ₀(q ₀-1). : q₀>2 n1 E R ⁿ 2nq ₀, p- p<₀. , f-[-, ]ⁿ, f A _p(R ⁿ) , _p([-, ]ⁿ) (1 << ).     

Limiting behavior of certain mixtures of distributions

U — [0, 1] Y — . X=[1–U ^1/v /Y], U Y.     

Arithmetic properties of the Markov function for the Jacobi weight

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Majorization versus power majorization

, . , [1]. 42.     

On the newly generalized absolute Riesz summability of orthogonal series

[3] , [1], ¦C,,(t)¦ _k - . , , ¦R, , (t)¦ _k - ¦R, , (t)¦ _k - . (t)=1,k=1 [7], [9].

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This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant#T 016 393.     

Generalization of some results concerning Walsh series and the dyadic derivative

, , , . , . , , x(0,1),x2^–j ,j=1,2,..., 2 ⁿ . , ka _k 0 k k. , (0, 1) , , , , . , .     

Converse results on equiconvergence of interpolating polynomials

, n- n- 1 , . , , ( « ») f .     

Central limit theorems for Walsh series with general gaps

. [1]. 3 - .     

Saturation theorems for discretized linear operators

, , , - .

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Part of this research was completed at a conference of Hungarian and American mathematicians held in Madison, Wisconsin, August 1974, and sponsored by the National Science Foundation (USA) and the Institute for Cultural Relations (Hungary).

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The first author gratefully acknowledges NSF support in Grant GP 19620.     

Morera type theorems on the unit disc

, . . : , , , , .     

On the equivalence of some rearrangements of the two-parameter Haar system

h ₁, L _p .

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This research was supported in part by MTA-NSF grants INT-8400708 and 8620153.     

Замечания о Сходкмости лагранжева интерполрования

( qP. )     

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.     

A generalized Laplace transform of generalized functions

- . . . , .     

О Тригонометрическом (0, 2)-Интерполировании

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О простых идеалах первой степени

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