Приближение функции ограниченнойp-флукту адии полиномами по мульти пликативным система м

A new discrete modulus of continuity is introduced for functions of boundedp-fluctuation, and direct and converse theorems are proved on the approximation of these functions by polynomials with respect to multiplicative systems. Sufficient conditions for the convergence of Fourier series with respect to multiplicative systems are also obtained and these are the best possible in a certain sense.

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. 60-     

A generalization of Pal-type interpolation

. .     

Transferring estimates for zonal convolution operators

_p - , . Ad- .     

On the almost everywhere convergence of double Fourier series of integrable functions

, . . Q _k [0,2],k=1,2, — . F(x, y)L(T), T=[0, 2]², G(x, y)L(T) , G(x,y)=F(x,y) Q=Q ₁ ×Q ₂ - .     

On the exactness of a theorem of G.A. Fomin

, . . [1] - . .     

О сравнительной теории простЫх чисел

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On summability of subsequences of partial sums of trigonometric Fourier series

n- (n1) fL ^p ([–, ] ⁿ ),=1 = (L C) . , , f([–, ] ⁿ ).     

A generalized integral with applications to trigonometric series

, . . .

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The authors wish to thank the referee whose comments improved the presentation of the paper. In fact, the present form of Lemma 2, which was originally very long, is due to the referee.     

Замечания о Сходкмости лагранжева интерполрования

( qP. )     

Converse results on equiconvergence of interpolating polynomials

, n- n- 1 , . , , ( « ») f .     

О простых идеалах первой степени

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Нормаляный поридок аддитявных арифметичыских функций на множестве дсдвинутых” пностых чясел

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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.     

Applications of matrix functions

A, ()=0, c(z)- T - TY=AY. A y(t)=y(, t) Ty=y Y(t). - c(T)y=0.     

On the parameter estimation of diffusional type processes with constant coefficients (Elementary Gaussian Processes)

, (1). 3, , ()=, (8) (16). [1], . (28) (31) ( 5), - (. [3]).

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The author thanks Professor M.Arató for having pointed out this problem, and for his valuable suggestions.     

On strong summability of polynomial expansions

—.

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Dedicated to Professor L. Leindler on his 50^th birthday     

On multivariate polynomialL 2-approximation to zero

, -, [–1,1] L ². - . , .     

Central limit theorems for Walsh series with general gaps

. [1]. 3 - .