Coproducts in the Category <Emphasis Type="Bold">M</Emphasis>κ<Emphasis Type="Bold">Frm</Emphasis>

The purpose of this paper is to study coproducts in the category MFrm (resp. M_cFrm), of metric -frames and uniform (resp. contractive) -frame maps. First, by applying the same technic that was used to find coproducts in Frm, we construct coproducts in the category Frm of -frames and -frame maps. Then, we define a metric diameter on the coproduct in Frm of a family of metric -frames and show that coproduct in Frm preserves metrizability.Mathematics Subject Classifications (2000) 06B23, 06D22, 18A30.     

On convex multipliers of convergence of some classes of bivariate fourier series

- ()N²,L _F ( ) — , 2- , {s _m() f} -L. — . (L _F( ),L _F( ) ={(k)} (kZ²) , fL_F( ) f , , L _F( ). - ={()} ={()} , n(())m()n(()+()) . R() , .. - . , . (L _F ( ),L _F ( )) , R(,)=O(1) (x).

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The author wishes to express his gratitude to S. A.Teljakovski for setting the problem and for his attention to this paper.     

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 .     

On power series with positive coefficients

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Some remarks on the approximation in the strong sense

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

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

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On an application of infinitely divisible distributions to quadrature problems

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Замечания о порядке погрещности интерполяции

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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.     

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

Идеологиыеское знаыение геометрии бояи—лобаыевского

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

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

On the approximation by rational combinations of a class of functions

() [0,1] — {(n)} — , +. , f(x) [0,1] () , x ₁ ,x ₂ [0, 1], (₁)=(₂), f(x ₁ )=f(x ₂ ).     

Orders of one-sided approximations of functions inL p -metric

. L _p , 0<p<, . , f, {E _n (f) _p } ₁ p>0 .

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The author expresses his thanks to S. B. Stekin for the attention he has paid to this work.     

On the order of approximation to functions ofH p (R) (0<p≦1) by certain means of Fourier integrals

H ^P (R ₊ ² ) — R ₊ ² ={zC: Imz>0} ^p (R) — H ^p (R ₊ ² ). P ^k (f,x) — ë- — ,W ^k (f,x) — — R ^k, (f,x) — f H (R) (. §1,1)–3)); _k (, f) _p — - . , fH ^p (R) 0<p1,kN; (1+)^–1<p1, 0<<,kN.     

Limiting behavior of certain mixtures of distributions

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

The order of magnitude of the arithmetic means of double orthogonal series

, - , (C, 1,1), (C, 1,0) (C, 0,1)- . , , . - .

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Dedicated to Academician S. M. Nikol'skii on his 80th birthday     

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] , (**), (*) .     

Maximal inequalities,convexity inequality,and their duality. II

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Majorization versus power majorization

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