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1.
2.
Classical theorems on differential inequalities [1, 2, 3] are generalized for initial value problems of the kind
and
where
is a singular Volterra operator,
is continuous and positive on ]a, b],
is a norm in R
n, and [u]+ and [u]– are respectively the positive and the negative part of the vector u R
n. 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.
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
6.
Let
be an entire function of finite type with respect to finite order
and let
be a subset of an open cone in a certain n-dimensional subspace
(the smaller
, the sparser
). We assume that this cone contains a ray
0} \right\}$$
" align="middle" border="0">
. It is shown that the radial indicator
of
at any point
may be evaluated in terms of function values at points of the discrete subset
. Moreover, if
tends to zero fast enough as
over
, then this function vanishes identically. To prove these results, a special approximation technique is developed. In the last part of the paper, it is proved that, under certain conditions on
and
, which are close to exact conditions, the function
bounded on
is bounded on the ray. 相似文献
7.
Suppose that k and l are integers such that
and
, M
k is a set of numbers without kth powers, and
. In this paper, we obtain asymptotic estimates of the sums
over
相似文献
8.
Let E be a normed space,
and
. Let
. We give some exact formulas for 7#x03C4;. 相似文献
9.
For an arbitrary function
, we determine the general form of a linear continuous functional on the space C
w
0
. The criterion for denseness of polynomials in the space
established by Hamburger in 1921 is extended to the spaces C
w
0
. 相似文献
10.
Let u(x) xR
q
be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p
x, (·) be the density of an R
q
valued canonical normal random variable with mean x and variance and let {G
x, ; (x, )R
q
×[0,1 ]} be the mean zero Gaussian process with covariance
A finite positive measure on R
q
is said to be in
with respect to u, if
When
, a multiple Wick product chaos
is defined to be the limit in L
2, as 0, of
where
,
denotes the Wick product of the m
j
normal random variables
.Consider also the associated decoupled chaos processes
,
defined as the limit in L
2, as 0, of
where
are independent copies of G
x,.Define
Note that a neighborhood of the diagonals of
in
is excluded, except those points on the diagonal which originate in the same Wick product in (i). Set
One of the main results of this paper is:
Theorem A. If
is continuous on (R
q
)
r
for all
then
is continuous on
.When u satisfies some regularity conditions simple sufficient conditions are obtained for the continuity of
on (R
q
)
r
. Also several variants of (i) are considered and related to different types of decoupled processes. These results have applications in the study of intersections of Lévy process and continuous additive functionals of several Lévy processes. 相似文献
11.
For entire Dirichlet series of the form
, we establish conditions under which the relation
holds uniformly in
outside a certain set E for which
where h() is a positive continuous function increasing to + on [0, +). 相似文献
12.
There are many studies on the asymptotic behavior of solutions of differential equations. In the present paper, we consider another aspect of this problem, namely, the rate of the asymptotic convergence of solutions. Let ϕ (t) be a scalar continuous monotonically increasing positive function tending to ∞ as t → ∞. It is established that if all solutions of a differential system satisfy the inequality
then the solution x(t; t
0, x
0) of this differential system tends to 0 faster than
.__________Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 137–142, January, 2005. 相似文献
13.
In the open disk
of the complex plane, we consider the following spaces of functions: the Bloch space
; the Hardy--Sobolev space
; and the Hardy--Besov space
. It is shown that if all the poles of the rational function R of degree n,
, lie in the domain
, then
, where
and
depends only on
. The second of these inequalities for the case of the half-plane was obtained by Semmes in 1984. The proof given by Semmes was based on the use of Hankel operators, while our proof uses the special integral representation of rational functions. 相似文献
14.
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
15.
We discuss purely singular finite-rank perturbations of a self-adjoint operator A in a Hilbert space . The perturbed operators
are defined by the Krein resolvent formula
, Im z 0, where B
z are finite-rank operators such that dom B
z dom A = |0}. For an arbitrary system of orthonormal vectors
satisfying the condition span |
i
} dom A = |0} and an arbitrary collection of real numbers
, we construct an operator
that solves the eigenvalue problem
. We prove the uniqueness of
under the condition that rank B
z = n. 相似文献
16.
Let
be i.i.d. random variables and let, for each
and
. It is shown that
a.s. whenever the sequence of self-normalized sums S
n
/V
n is stochastically bounded, and that this limsup is a.s. positive if, in addition, X is in the Feller class. It is also shown that, for X in the Feller class, the sequence of self-normalized sums is stochastically bounded if and only if
相似文献
17.
We study sets
there exist n projectors P1,...,Pn such that
. We prove that if n 6, then
. 相似文献
18.
Estimates for deviations are established for a large class of linear methods of approximation of periodic functions by linear combinations of moduli of continuity of different orders. These estimates are sharp in the sense of constants in the uniform and integral metrics. In particular, the following assertion concerning approximation by splines is proved: Suppose that
is odd,
. Then
moreover, for
it is impossible to decrease the constants on
. Here,
are some explicitly constructed constants,
is the modulus of continuity of order r for the function f, and
are explicitly constructed linear operators with the values in the space of periodic splines of degree
of minimal defect with 2n equidistant interpolation points. This assertion implies the sharp Jackson-type inequality
. Bibliography: 17 titles. 相似文献
19.
Yu. V. Nagrebetskaya 《Algebra and Logic》2000,39(6):396-406
We study into the question of whether some rings and their associated matrix rings have equal decidability boundaries in the scheme and scheme-alternative hierarchies. Let
be a decidability boundary for an algebraic system A; w.r.t. the hierarchy H. For a ring R, denote by
an algebra with universe
. On this algebra, define the operations + and in such a way as to extend, if necessary, the initial matrices by suitably many zero rows and columns added to the underside and to the right of each matrix, followed by ordinary addition and multiplication of the matrices obtained. The main results are collected in Theorems 1-3. Theorem 1 holds that if R is a division or an integral ring, and R has zero or odd characteristic, then the equalities
hold for any n1. And if R is an arbitrary associative ring with identity then
for any n 1 and i,j { 1,..., n}, where e
ij
is a matrix identity. Theorem 2 maintains that if R is an associative ring with identity then
. Theorem 3 proves that
for any n 1. 相似文献
20.