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1.
In what follows, $C$ is the space of
-periodic continuous functions; P is a seminorm defined on C, shift-invariant, and majorized by the uniform norm;
is the mth modulus of continuity of a function f with step h and calculated with respect to P;
,
(
),
,
,
Theorem 1.
Let
. Then
For some values of
and seminorms related to best approximations by trigonometric polynomials and splines in the uniform and integral metrics, the inequalities are sharp. Bibliography: 6 titles. 相似文献
2.
O. L. Vinogradov 《Journal of Mathematical Sciences》2003,114(5):1608-1627
Let
be the space of 2-periodic functions whose (r – 1)th-order derivative is absolutely continuous on any segment and rth-order derivative belongs to L
p, S
2n,m
is the space of 2-periodic splines of order m of minimal defect over the uniform partition
. In this paper, we construct linear operators
such that
where
To construct the operators X
n,r,m, we use the same idea as in the polynomial case, i.e., the interpolation of Bernoulli kernels. As is proved, the operators X
n,r,m converge to polynomial Akhiezer–Krein–Favard operators as
. Bibliography: 10 titles. 相似文献
3.
O. L. Vinogradov 《Journal of Mathematical Sciences》2001,107(4):3987-4001
In what follows, C is the space of
-periodic continuous real-valued functions with uniform norm,
is the first continuity modulus of a function
with step h, H
n is the set of trigonometric polynomials of order at most n,
is the set of linear positive operators
(i.e., of operators such that
for every
),
is the space of square-integrable functions on
,
It is proved that
coincides with the smallest eigenvalue of some matrix of order n+1. The main result of the paper states that, for every
does not exceed and, for
, is equal to the minimum of the quadratic functional
over the unit sphere of
. Then it is calculated that
Bibliography: 19 titles. 相似文献
4.
This article improves results of Hamada, Helleseth and Maekawa on minihypers in projective spaces and linear codes meeting the Griesmer bound.In [10,12],it was shown that any
-minihyper, with
, where
, is the disjoint union of
points,
lines,...,
-dimensional subspaces. For q large, we improve on this result by increasing the upper bound on
non-square, to
non-square,
square,
, and (4) for
square, p prime, p<3, to
. In the case q non-square, the conclusion is the same as written above; the minihyper is the disjoint union of subspaces. When q is square however, the minihyper is either the disjoint union of subspaces, or the disjoint union of subspaces and one subgeometry
. For the coding-theoretical problem, our results classify the corresponding
codes meeting the Griesmer bound. 相似文献
5.
O. L. Vinogradov 《Journal of Mathematical Sciences》2004,120(5):1662-1671
Let
be the Jacobi polynomials and let C[a,b] be the space of continuous functions on [a,b] with the uniform norm. In this paper, we study sequences of Lebesgue constants, i.e., of the norms of linear operators
generated by a multiplier matrix
defined by the following relations:
and
In the case || = || = 1/2, we prove the following statements for the Jacobi polynomials (these statements are similar to known results for the trigonometrical system). Consider the cases
and
Under some conditions on a function , the values
and
equal
and
In addition, we show that for the Fourier–Legendre summation methods ( = = 0) generated by the multiplier function
, the limit and supremum of the sequence of Lebesgue constants may differ. Bibliography: 11 titles. 相似文献
6.
A. N. Petrov 《Journal of Mathematical Sciences》2001,107(4):4067-4072
A new numerical inequality for average power means is presented. Let
and let
be a sequence of positive numbers. Consider the operator
. We denote by
the superposition of these operators. The following assertion is proved: if
. Bibliography: 2 titles. 相似文献
7.
O. M. Fomenko 《Journal of Mathematical Sciences》2003,118(1):4918-4932
Let
be the class number of properly equivalent primitive binary quadratic forms
of discriminant
. The case of indefinite forms
is considered. Assuming that the extended Riemann hypothesis for some fields of algebraic numbers holds, the following results are proved. 1. Let
be an arbitrarily slow monotonically increasing function such that
. Then
where
. 2. Let F be an arbitrary sufficiently large positive constant. Then for
x_F$$
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, the relation
holds. 3. The relation
holds, where A is Artin's constant. Hence, for the majority of discriminants of the form
, where
, the class numbers are small. This is consistent with the Gauss conjecture concerning the behavior of
for the majority of discriminants
0$$
" align="middle" border="0">
in the general case. Bibliography: 22 titles. 相似文献
(\log p)^{\alpha (p)} } \right\} = o(\pi (x)),$$ " align="middle" vspace="20%" border="0"> |
F} \right\} \asymp \frac{{\pi (x)}}{F}$$ " align="middle" vspace="20%" border="0"> |
8.
O. M. Fomenko 《Journal of Mathematical Sciences》2003,118(1):4910-4917
Let
be the Hecke eigenbasis of the space
of
-cusp forms of weight 2. Let p be a prime. Let
be the Hecke L-series of form
. The following statements are proved:
and
We also give a correct proof of a previous author's theorem on automorphic L-functions. Bibliography: 12 titles. 相似文献
9.
Suppose that X is a Banach space, K denotes the set of real numbers R or the set of nonnegative real numbers R
{+},
is a family of linear operators from X into X such that T
0=I is the identity operator in X,
for all
, and there exists M such that
for all
. The expression
is called the rth order modulus of continuity of an element x with step h in the space X with respect to the family A(K). The properties of
are studied. Bibliography: 3 titles. 相似文献
10.
The paper deals with the problem of recovering the parameters (functions)
and
of the Maxwell dynamical system
(tan is the tangent component;
is a solution) by the response operator
(
is the normal). The parameters determine the velocity
, the c-metric
, and the time
. It is shown that for any fixed
, the operator
determines
and
in
uniquely. Bibliography: 15 titles. 相似文献
11.
Let P
k be a path on k vertices. In an earlier paper we have proved that each polyhedral map G on any compact 2-manifold
with Euler characteristic
contains a path P
k such that each vertex of this path has, in G, degree
. Moreover, this bound is attained for k = 1 or k 2, k even. In this paper we prove that for each odd
, this bound is the best possible on infinitely many compact 2-manifolds, but on infinitely many other compact 2-manifolds the upper bound can be lowered to
. 相似文献
12.
Guo Xin WEI 《数学学报(英文版)》2007,23(6):1075-1082
In this paper, we give a characterization of tori S^1 ( √ nr+2-n/nr)×S^n-1(√ n-2/nr) and S^m ( √n/m ) ×S^n-m (√n-m/n). Our result extends the result due to Li (1996)on the condition that M is an n-dimensional complete hypersurface in Sn+1 with two distinct principal curvatures. Keywords principal curvature, Clifford torus, Gauss equations 相似文献
13.
G. P. Kukhta 《Journal of Mathematical Sciences》1992,60(2):1396-1398
By the Fourier method a solution of the equation
相似文献
14.
M. B. Zwyagina 《Journal of Mathematical Sciences》2002,112(4):4337-4347
Some applications of the general theorem on the existence of local duality for modules over Noetherian commutative rings are given. Let
be a Noetherian commutative ring, let
be a set of maximal ideals in
, and let
. Then the category of Artinian modules is dual to the category of Noetherian modules. Several structural results are proved, including the theorem on the structure of Artinian modules over principal ideal domains. For rings of special kinds, double centralizer theorems are proved. Bibliography: 5 titles. 相似文献
15.
The following classes of functions analytic in the unit disk are considered:
16.
17.
Let (x) = A(x)
, where A(x) denotes the number of square-full integers not exceeding x. In this paper, we prove that (x) = O
, which improves the exponent 4/27 obtained by Y.-C. Cai [5]. 相似文献
18.
Andreas Rosenschon 《K-Theory》1999,16(2):185-199
Let X be a smooth projective variety over the complex numbers. We consider the cohomology of the sheaves
and
arising from Deligne–Beilinson cohomology and the Hodge filtration on the singular cohomology of X. We show that one can identify
with the image of the truncated regulator map c¯2,1. In particular, this implies that
is countable. Since this group is a direct summand of coker
, this gives a partial answer to Voisin's conjecture that cocker() is countable. In the case of X a surface, we prove that the Albanese kernel T(X) is isomorphic to the group of global sections of
if and only if pg=0. 相似文献
19.
A Littlewood-Paley type
inequality 总被引:2,自引:0,他引:2
In this note we prove the following theorem: Let u be a
harmonic function in the unit ball
and
. Then there is a
constant C =
C(p,
n) such that
20.
V. V. Makeev 《Journal of Mathematical Sciences》2003,113(6):812-815
A class of centrally-symmetric convex 12-topes (12-hedrons) in
is described such that for an arbitrary prescribed norm
on
each polyhedron in the class can be inscribed in (circumscribed about) the
-ball via an affine transformation, and this can be done with large degree of freedom. Bibliography: 5 titles. 相似文献
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