共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
4.
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
5.
The Plücker embedding of the complex projective space
in the Grassmannian
of bivectors is used for proving several theorems on the relationship between the complex structure of
and its Riemannian geometry. It is shown that the separation set of
in the Plücker model is the face of
for a certain calibration. Bibliography: 11 titles. 相似文献
6.
S. Ya. Novikov 《Journal of Mathematical Sciences》2004,120(5):1733-1751
We study operators
(not necessarily linear) defined on a quasi-Bahach space X and taking values in the space of real-valued Lebesgue-measurable functions. Factorization theorems for linear and superlinear operators with values in the space
are proved with the help of the Lorentz sequence spaces
. Sequences of functions belonging to fixed bounded sets in the spaces
are characterized for
and
. The possibility of distinguishing weak type operators (bounded in the space
) from operators factorizable through
is obtained in terms of sequences of independent random variables. A criterion under which an operator is symmetrically bounded in order in
, is established. Some refinements of the above-mentioned results are obtained for translation shift-invariant sets and operators. Bibliography: 30 titles. 相似文献
7.
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
8.
R. N. Karasev 《Journal of Mathematical Sciences》2001,104(4):1293-1300
Let
be a family of translations of a convex compact set
such that every two elements of
have a common point. Then there exist three points
such that each element of
contains one of these points. This answers in the affirmative an old question by Grünbaum. Bibliography: 13 titles. 相似文献
9.
E. G. Emel'yanov 《Journal of Mathematical Sciences》2002,110(6):3078-3090
An extension of a theorem on extremal decomposition of a Riemann surface is obtained. The problem of extremal decomposition is extended from the case of a Riemann surface
with a prescribed set
of distinguished points to the case of the Teichmüller space
corresponding to
under quasiconformal homeomorphisms f. For the functional
of our problem on extremal decomposition of a surface
, we consider a function
expressing the dependence of the extremal value of
on a point
. Differentiation formulas for the function
are derived. These formulas are different and depend on the genus g of the surface
. The case where the function
is pluriharmonic is considered. Bibliography: 8 titles. 相似文献
10.
A. N. Frolov 《Journal of Mathematical Sciences》2002,109(6):2229-2240
Let
be a sequence of independent equidistributed random vectors with
. Let
, where
and
denotes the indicator function of the event in brackets. If, for example,
are the gains and
are the indicators of success in repetitions of a game of chance, then
is the maximal gain along head runs (sequences of successes without interruptions) of length j. We investigate the asymptotic behavior of the values
,
, where
is the length of the longest head run in
. We show that the asymptotics of the values
depend significantly on the growth rate of j and that these asymptotics vary from the strong noninvariance (as in the ErdsRéenyi law of large numbers) to the strong invariance (as in the CsöorgRévész strong approximation laws). We also consider the Shepp-type statistics. Bibliography: 17 titles. 相似文献
11.
M. B. Zvyagina 《Journal of Mathematical Sciences》2004,120(4):1591-1602
Let
be an associative ring with identity, and let
be the category of left unitary
-modules. A complete characterization of continuous additive co- and contravariant functors
is given. Such functors are either representable, or equivalent to a tensor product, or trivial ones. The class of categories that are dual to
and, therefore, are equivalent to the category of compact right
-modules is constructed by purely algebraic means. A canonical category is singled out in this class. A purely algebraic structure that is equivalent to the topology-algebraic structure of compact right
-modules is constructed. Algebraic analogs of connection and complete disconnection are given. Bibliography: 6 titles. 相似文献
12.
Markov- and Bernstein-Type Inequalities for Polynomials with Restricted Coefficients 总被引:1,自引:0,他引:1
The Markov-type inequality
is proved for all polynomials of degree at most n with coefficients from {-1,0,1} with an absolute constant c. Here ·[0,1] denotes the supremum norm on [0,1]. The Bernstein-type inequality
is shown for every polynomial p of the form
The inequality
is also proved for every analytic function p on the open unit disk D that satisfies the growth condition
相似文献
13.
V. A. Zalgaller 《Journal of Mathematical Sciences》2001,104(4):1255-1258
Let
be nonempty convex bodies in
. Let
be vectors in
, let
, and let
. Then
is a convex set, and the family of sets
is concave. Let
. Then for the mean cross-sectional measures W_v (\Phi (\rho )),
, the functions
are concave on D. (Note that % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca% WGxbWaaSbaaSqaaiaaicdaaeqaaOGaaiikaiabfA6agjaacIcacqaH% bpGCcaGGPaGaaiykaiabg2da9iaabAfacaqGVbGaaeiBamaaBaaale% aatCvAUfKttLearyqr1ngBPrgaiuGacqWFRbWAaeqaaOGaeuOPdyKa% aiikaiabeg8aYjaacMcaaaa!4EE7!\[W_0 (\Phi (\rho )) = {\text{Vol}}_k\Phi (\rho )\] is the k-volume.) Bibliography: 2 titles. 相似文献
14.
This paper considers the approximation of the Kantorovich–Shepard operators in
spaces for
. For
the Kantorovich–Shepard operators
are defined by (1.1). Then
where
is a positive number depending only on
and , and $$ \varepsilon_{n} =\cases{ n^{-1}, & if \
2$$
" align="middle" border="0">
; \cr\nosm n^{-1}\log n, & if \
; \cr\nosm n^{1-\lambda}, & if \
. \cr} $$ 相似文献
15.
A. I. Generalov 《Journal of Mathematical Sciences》2004,120(4):1563-1574
A relative version of Rickard's theorem is proved, namely, if is a quasi-Frobenius proper class of short sequences in an Abelian category
, then the -stable category of the category
is a quotient category of the relative bounded derived category
(
). Bibliography: 20 titles. 相似文献
16.
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
17.
A. K. Prykarpatsky D. L. Blackmore Ya. V. Mykytyuk 《Journal of Mathematical Sciences》2001,104(5):1411-1421
This article is a continuation of [J. Math. Sci., 99, No.5, 1541–1547 (2000)] devoted to the validity of the Lax formula (cited in the article of Crandall, Ishii, and Lions [Bull. AMS, 27, No.1, 1–67 (2000)])
for a solution to the Hamilton–Jacobi nonlinear partial differential equation
where the Cauchy data
are now a function semicontinuous from below,
is the usual norm in
,
, and
is a positive evolution parameter. We proved that the Lax formula solves the Cauchy problem (2) at all points
,
fixed save for an exceptional set of points R of the F
type, having zero Lebesgue measure. In addition, we formulate a similar Lax-type formula without proof for a solution to a new nonlinear equation of the Hamilton–Jacobi-type:
where
is a diagonal positive-definite matrix, mentioned in Part I and having interesting applications in modern mathematical physics. 相似文献
18.
The paper deals with the system
where
and
are
-matrix functions;
is a boundary control;
is the solution. The singularities of the fundamental solution corresponding to the controls
(
is the Dirac
-function) are under investigation. In the case of
, the singularities of the fundamental solution are described in terms of the standard scale
. In the presence of points
an interesting effect occurs: singularities of intermediate (fractional) orders appear. Bibliography: 1 title. 相似文献
19.
O. V. Sarafanov 《Journal of Mathematical Sciences》2004,120(2):1195-1239
The C
*-algebra
generated by the operators of pseudodifferential boundary value problems on a manifold
with smooth closed disjoint edges and boundary
is studied. The operators act in the space L
2(
)
L
2(
). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra
Bibliography: 12 titles. 相似文献
20.
V. V. Lebedev 《Functional Analysis and Its Applications》2002,36(1):25-29
We consider the algebra
of absolutely convergent Fourier series on the circle
. According to the Beurling–Helson theorem, the condition
, implies that
is trivial:
. We construct a nontrivial diffeomorphism
of
onto itself such that
, where (n) is an arbitrary given sequence with
. By analogy with a conjecture due to Kahane, it is natural to suppose that this rate of growth is the slowest possible. 相似文献