The Cesàro-Denjoy-Bochner scale of almost periodicity

, —— , . , f, ——, —. .     

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.     

Continuation of functionals on ultradifferentiable function spaces

, c _k b _k . . . .

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This work is supported by N.B.H.M. grant No. 48/1/94-R&D-II.     

On an inequality of Longnecker and Serfling

— [2], [5], [7], [8], , , . , . , .     

Investigation of Haar and Franklin series in Hardy spaces

(L ¹,H) (, ) , ; H — . , , L ¹ . [13] , . , , , .     

A generalized Laplace transform of generalized functions

- . . . , .     

Extension of functions,which are traces of functions belonging to 249-01249-01249-01on an arbitrary subset of the line

( , k) , ER f(x) f(x)H _k (R) (k2— ,=(t) — k- ). f(x) E (t).     

Converse results on equiconvergence of interpolating polynomials

, n- n- 1 , . , , ( « ») f .     

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.     

Zeros in tables of characters for the groups Sn and An

In the representation theory of symmetric groups, for each partition of a natural number n, the partition h() of n is defined so as to obtain a certain set of zeros in the table of characters for S_n. Namely, h() is the greatest (under the lexicographic ordering ) partition among P(n) such that (g) 0. Here, is an irreducible character of S_n, indexed by a partition , and g is a conjugacy class of elements in S_n, indexed by a partition . We point out an extra set of zeros in the table that we are dealing with. For every non self-associated partition P(n), the partition f() of n is defined so that f() is greatest among the partitions of n which are opposite in sign to h() and are such that (g) 0 (Thm. 1). Also, for any self-associated partition of n > 1, we construct a partition () P(n) such that () is greatest among the partitions of n which are distinct from h() and are such that (g) 0 (Thm. 2).Supported by RFBR grant No. 04-01-00463 and by RFBR-BRFBR grant No. 04-01-81001.Translated from Algebra i Logika, Vol. 44, No. 1, pp. 24–43, January–February, 2005.     

On the distribution of points of maximal deviation in complex Čebyšev approximation

f — , . p _n (f) f . , n+2 , f–p _n (f) . , n . , .

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On the distribution of points of maximal deviation in complex ebyev approximation

     

On Szalay's theorem of double series

[1] . , [1] .     

On the angular derivative and univalence

f . , , — , A f f(). , , f() 0 . , , ,A , f . , f() - f() . , , . (1976) ( ¦f(z)¦<1) . . (1969) ( ).     

Pointwise convergence of expansions with respect to certain product systems

- , - _n A_n-,. , . , ¦_n¦=1 (n=1,2, ), . , — — , .     

Spectral orders and convolution

. (R) _{– –} fg(y)h(x–y) dx dy _{– –} f ^{^} (x)g ^{^} (y)h ^{^} (x–y)dx dy (f,g0) —:f×gf ^{^} ×g ^{^}(f,g 0) f^{^} g^{^} f g -, X — . , - f ₁f ₂ , f ₁ ^{^} ×gf ₂×g 0g. .     

On imbedding of certain function classes in symmetric spaces

2— - , () — - (), (, ) (0< <)— - . , >1; ; > ; ₁(), ₂() — -;f(x) — —. , () — ( , X, L , , ( ) -.

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The author thanks Prof. M. K. Potapov for having proposed the problem and for the help he has given in the work.     

Exact estimates for partially monotone approximation

f(x) — , - [–1,1], (f, ) — , as— f, . . (- ) (x _i,x _{i+ 1}) (i=0, 1, ...,s–1; =–1,x _s,=1), f(x) . , n=0,1,... _n() , [– 1,1] signf(x) sign _n(x) 0, ¦f(x)– _n(x)¦ C(s) (f, 1/n+1, C(s) s. , - , « » .     

On unconditionally convergent basis expansions in the space of continuous functions

[0,1], - H .

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This paper was written during the author's scholarship at the State University of Odessa in the USSR.     

Orthonormal systems satisfying an inequality of S. M. Nikol'skii

N- (p, q) (1 pN-, L _p - L _q -. , , , L L _q - , , .     

Limiting behavior of certain mixtures of distributions

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