Intrinsic definition of the Colombeau algebra of generalized functions

— G (), . . . , : , , D()G(), , , G(), , , , — .     

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.     

On cubature formulas on the basis of lattices

Q (.. , L). Q . P(S_r(2)) — 2 (S _r(2) (r — ). , M(P(S _r(m=sup{t(·)t(·)₁:t P(S _r(2)),t 0}. , /4+(1)M(P(S _r(2)))/r ²15/17+(1)(r+). (Q), Q L.     

On summability of subsequences of partial sums of trigonometric Fourier series

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

The Cesàro-Denjoy-Bochner scale of almost periodicity

, —— , . , f, ——, —. .     

Radon—Nikodym theorems for multimeasures and transition multimeasures

— . , — . , .

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Research supported by N. S. F. Grant DMS-8802688.     

Orthogonal systems invariant under an automorphism

, , - ( ) . , - , ( ) .     

Some inequalities of Hardy-Littlewood type

[3] , >0 n ^– a _n , . , . . , .

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This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant #234.     

Inversion and structure formulae for a generalized Laplace transform

, D_v(.) , .     

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.     

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

Conditions for the existence of stieltjes integral of functions of bounded generalized variation

, , , , - , , , , . . . .     

On approximation of functions on the half-line by algebraic polynomials

, . , .     

О простых идеалах первой степени

.      

Fortsetzungssätze und Moduln über Semifields

. . — . — —.

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Herrn Professor Dr. Frank Terpe zum 60. Geburtstag gewidmet     

Inequalities of Hardy-Littlewood type

( ). - .     

On the asymptotic distribution of oscillation points in rational approximation

. . ( ) , , (m) (m)m, n(m) ^* ) ( d(m) — r _{m, n(m)} ^*) )/ , .

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The paper was written during the second author's visit at the Mathematical Institute of the Hungarian Academy of Sciences.     

On the approximation of discrete functions by fourier-hahn sums

— f: {0,1, ..., N–1}R. .     

Замечание О Механичецкой Квадратуре

.      

On an inequality of Longnecker and Serfling

— [2], [5], [7], [8], , , . , . , .