共查询到20条相似文献,搜索用时 31 毫秒
1.
We consider the series
and
whose coefficients satisfy the condition
for
, where the sequence
can be expressed as the union of a finite number of lacunary sequences. The following results are obtained. If
as
, then the series
is uniformly convergent. If
for all
, then the sequence of partial sums of this series is uniformly bounded. If the series
is convergent for
and
as
, then this series is uniformly convergent. If the sequence of partial sums of the series
for
is bounded and
for all
, then the sequence of partial sums of this series is uniformly bounded. In these assertions, conditions on the rates of decrease of the coefficients of the series are also necessary if the sequence
is lacunary. In the general case, they are not necessary. 相似文献
2.
We study nonlinear elliptic systems of the form
,
even,
, with the natural energy space
. We establish that for
solutions from
belong to the Morrey space and the Morrey exponent does not tend to zero under the degeneration of ellipticity. In the case
, a similar result is obtained under an additional structure condition on the system. 相似文献
3.
The well-known theorem of Weyl about the essential self-adjointness of the Sturm--Liouville operator
in
with
, and
is generalized to second-order elliptic operators in
. The multidimensional Weyl theorem is derived from a more general theorem; to state and prove the latter, a special covering family is constructed. The results obtained imply the known multidimensional analogs of the Weyl theorem and, unlike these analogs, apply to open proper subsets
in
. 相似文献
4.
We obtain necessary and sufficient conditions for the solvability of the augmentation and modification problems of order
for Hermitian matrices. The augmentation problem consists in the construction of a Hermitian
-matrix with a given
-block
in block
-representation and with the prescribed eigenvalues. The modification problem consists in the construction of a Hermitian
-matrix
of rank not greater than
so that the obtained matrix, being added to a given Hermitian
-matrix
, will have the required spectrum. We give an estimate for the minimal number of different eigenvalues of the solutions to these problems. 相似文献
5.
Two numerical characteristics of a nonrectifiable arc
generalizing the notion of length are introduced. Geometrically, this notion can naturally be generalized as the least upper bound of the sums
, where
are the lengths of segments of a polygonal line inscribed in the curve
and
is a given function. On the other hand, the length of
is the norm of the functional
in the space
; its norms in other spaces can be considered as analytical generalizations of length. In this paper, we establish conditions under which the generalized geometric rectifiability of a curve
implies its generalized analytic rectifiability. 相似文献
6.
We introduce the notions of a Gibbs measure with the corresponding potential with association
(where
is a subset of the set
) of a Markov random field with memory
and measure with association
. It is proved that these three notions are equivalent. 相似文献
7.
For a given homogeneous elliptic partial differential operator
with constant complex coefficients, two Banach spaces
and
of distributions in
, and compact sets
and
in
, we study joint approximations in the norms of the spaces
and
(the spaces of Whitney jet-distributions) by the solutions of the equation
in neighborhoods of the set
. We obtain a localization theorem, which, under certain conditions, allows one to reduce the above-cited approximation problem to the corresponding separate problems in each of the spaces. 相似文献
8.
It is proved that if a normal semifinite weight on a von Neumann algebra
satisfies the inequality
for any selfadjoint operators
in
, then this weight is a trace. Several similar characterizations of traces among the normal semifinite weights are proved. In particular, Gardner's result on the characterization of traces by the inequality
is refined and reinforced. 相似文献
9.
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
10.
We obtain sufficient conditions for the continuity of the general nonlinear superposition operator (generalized Nemytskii operator) acting from the space
of differentiable functions on a bounded domain
to the Lebesgue space
. The values of operators on a function
are locally determined by the values of both the function
itself and all of its partial derivatives up to order
inclusive. In certain particular cases, the sufficient conditions obtained are proved to be necessary as well. The results are illustrated by several examples, and an application to the theory of Sobolev spaces is also given. 相似文献
11.
Let
be a sequence of complex numbers such that
as
. For
close to the imaginary axis, upper bounds of the indicator of a nonzero entire function of exponential type with minimal growth vanishing on
is obtained. These bounds give sufficient conditions for the system of exponents
to be incomplete in an unbounded domain in
. 相似文献
12.
We consider the extremal problem to determine the maximal number
of columns of a 0-1 matrix with
rows and at most
ones in each column such that each
columns are linearly independent modulo
. For fixed integers
and
, we shall prove the probabilistic lower bound
=
; for
a power of
, we prove the upper bound
which matches the lower bound for infinitely many values of
. We give some explicit constructions. 相似文献
13.
Let
be a closed orientable surface of genus
, endowed with the structure of a Riemann manifold of constant negative curvature. For the universal covering
, there is the notion of absolute, each of whose points determines an asymptotic direction of a bundle of parallel equidirected geodesics. In the paper it is proved that there is a set
on the absolute having the cardinality of the continuum and such that if an arbitrary flow on
has a semitrajectory whose covering has asymptotic direction defined by a point from
, then this flow is not analytical and has infinitely many stationary points. 相似文献
14.
Suppose that
is an arbitrary finite complex Borel measure on the interval
is its Poisson integral,
and
are the conjugate harmonics of
, and
is the nontangential limiting value of the analytic function
as
. In this paper, we consider the problem of representing the analytic function
in terms of its boundary values
. 相似文献
15.
We construct the trajectory attractor
of a three-dimensional Navier--Stokes system with exciting force
. The set
consists of a class of solutions to this system which are bounded in
, defined on the positive semi-infinite interval
of the time axis, and can be extended to the entire time axis
so that they still remain bounded-in-
solutions of the Navier--Stokes system. In this case any family of bounded-in-
solutions of this system comes arbitrary close to the trajectory attractor
. We prove that the solutions
are continuous in t if they are treated in the space of functions ranging in
. The restriction of the trajectory attractor
to
,
, is called the global attractor of the Navier--Stokes system. We prove that the global attractor
thus defined possesses properties typical of well-known global attractors of evolution equations. We also prove that as
the trajectory attractors
and the global attractors
of the
-order Galerkin approximations of the Navier--Stokes system converge to the trajectory and global attractors
and
, respectively. Similar problems are studied for the cases of an exciting force of the form
depending on time
and of an external force
rapidly oscillating with respect to the spatial variables or with respect to time
. 相似文献
16.
We prove the absolute continuity of the spectrum of the Schrödinger operator in
,
, with periodic (with a common period lattice
) scalar
and vector
potentials for which either
,
, or the Fourier series of the vector potential
converges absolutely,
, where
is an elementary cell of the lattice
,
for
, and
for
, and the value of
is sufficiently small, where
and
otherwise,
, and
. 相似文献
17.
A. Yu. Makovetskii 《Journal of Mathematical Sciences》2003,113(6):818-821
Oriented special spines of 3-manifolds are studied. (Orientation is an additional structure on the spine, and each 3-manifold possesses a special spine with such a structure.) The transformations (moves)
and
of special spines, which do not change the manifold, are well known. It is proved that
and
preserve orientability of a spine, while
and
do not. For spines of homology balls, a class of moves is described allowing one to pass from a given orientation of a spine to any other orientation of the spine. Bibliography: 6 titles. 相似文献
18.
V. V. Kornienko 《Mathematical Notes》2000,68(5-6):576-587
We study the distribution in the complex plane
of the spectrum of the operator
, generated by the closure in
of the operation
originally defined on smooth functions
with values in a Hilbert space
satisfying the Dirichlet conditions
. Here
and A is a model operator acting in
. Criterial conditions on the parameter
for the eigenfunctions of the operator
to form a complete and minimal system as well as a Riesz basis in the Hilbert space H are given. 相似文献
19.
Frank Filbir Roland Girgensohn Anu Saxena Ajit Iqbal Singh Ryszard Szwarc 《Journal of Computational Analysis and Applications》2000,2(2):177-213
For an orthogonal polynomial system
and a sequence
of nonzero numbers,let
be the linear operator defined on the linear spaceof all polynomials via
for all
.We investigate conditions on
and
under which
can simultaneously preserve the orthogonality ofdifferent polynomial systems. As an application, we get that for
, a generalized Laguerre polynomial system, no
can simultaneously preserve the orthogonality of twoadditional Laguerre systems,
and
, where
and
. On the other hand, for
,the Chebyshev polynomial system and
,
simultaneously preserves the orthogonality of uncountablymany kernel polynomial systems associated with p. We study manyother examples of this type. 相似文献
20.
On the basis of the Kharitonov theorem, sufficient conditions on an
matrix A are presented for the matrix
to be stable for arbitrary
,
. 相似文献