On Szalay's theorem of double series

[1] . , [1] .     

Some remarks on the approximation in the strong sense

. , , , , . , . , , .

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On the 70th birthday of Professor S. M. Nikol'skii     

Generalized localization and convergence tests for double trigonometric Fourier series of functions fromL p,p>1

. E , f(x)L _p (T ^N ),P1,f(x)=0 E (E— ^N =[-, ]^N) E , . , .

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In closing the author thanks V. A. Il'in and . A. Alimov for their constant attention paid to the present work.     

Thep-adic differential-integral type operator

, p- , , , , , , . —p- - — , . , , .. , .     

The absolute generalized harmonic-Cesàro summability of a Fourier series

[8] . , , [2] , . - , , , . .     

A generalization of the Heine limit for functions which converge on a base

. , , . . . .     

On a problem of B. I. Golubov

. . . : s_n(x) — , _n-(, 1)- n L ². , . , : a _k l ² _n () [0,1] , (*) , (**) . a _k l ² u _n () [0,1] , (**), (*) .     

A comparison of uniform and discrete polynomial approximation

- , . .     

On contiguity of probability measures corresponding to semimartingales

, (ⁿ), - (P ⁿ ), P ⁿ (A ⁿ )>0P ⁿ (A ⁿ )0,n. [15] - , . , P ⁿ P ⁿ T ⁿ T ⁿ .     

Some expansion formulae for Fox'sH-function of two variables involving associated Legendre functions

H- .     

Perfect splines of least uniform deviation

(v _k) ₁ ⁿ , 1v _kr, v₁+...+v_n r, p(;r) — =(x ₁,v ₁),...,(x _n,v _n), v _1+...+v _n-r ^(r(;·)=1. , (^*;t) [, ] (;t) _{x 1}<... n v ₁ ...,v _n. (^*;t) .     

On extremal subspaces and approximation of periodic functions by splines of minimal defect

. . , 320 625 . 72      

Trigonometric Cesàro bases in the spaces of functions integrable with power weight

(2), k1, >0, L _p (0,), 1p L =C. , , p, k, (C, )- L _p (0,), , , {sinnx} _n ^=k/ (C, )- L _p (0,) |x|^p . , 1p, {x sinnx} _n=k , k2 2k–2–1/p<2k–1/p, (C, )- L ^p [0,] , >–(p–1)/.     

Rate of approximation by rectangular partial sums of double orthogonal series

( ) . .

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Dedicated to Professor K. Tandori on his seventieth birthday

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This research was supported in part by Grant # K41 100 of the Joint Fund of the Government of Ukraine and the International Science Foundation.     

A matrix generalization of a theorem of SzegŐ

— -B T . , T, T. — T, .., d=1. - . Cere: 0<p< exp logd=inf ¦1–t¦ ^p d, t , t(0)=0., . . . . . , . [1]. , . p=2 . - . p=2 [6, 8]. — p.     

On the notion of measurability

. , . , . , , - , . , , - .

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I wish to record my thanks to Dr. Kummer for his constant encouragement and many helpful suggestions in preparing this paper.     

Hardy spaces of predictable martingales

, P _p Q _p .

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This research was partially supported by the Hungarian Scientific Foundation.     

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.     

Summability of multiple Fourier series. Growth of Lebesgue constants

. , . . , H ₂ . , .     

On ortbogonal polynomial bases in the spacesC andL

, >0 C L - ( ) {Q _n(x)} , Q _n (x)–v _n n ¹⁺ nn ₀ (). , =0.