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1.
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
2.
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
3.
In this paper, we consider equations of the form
, where
is a function with values in the Hilbert space
, the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in
. The linear operator
generating the C
0-semigroup in the energy space
is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms. 相似文献
4.
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
5.
Aderemi Kuku 《K-Theory》2001,22(4):367-392
Let
be a rational prime,
an exact category. In this article, we define and study for all
, the profinite higher K-theory of
, that is
as well as
, where
is the
-dimensional mod-
Moore space. We study connections between
and prove several
-completeness results involving these and associated groups including the cases where
is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory
of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of . 相似文献
6.
S. Yu. Orevkov 《Mathematical Notes》2000,68(5-6):588-593
Dehornoy constructed a right invariant order on the braid group B
n uniquely defined by the condition
1{\text{ if }}\beta _0 ,\beta _1$$
" align="middle" border="0">
are words in
. A braid is called strongly positive if
1$$
" align="middle" border="0">
for any
. In the present paper it is proved that the braid
is strongly positive if the word
does not contain
. We also provide a geometric proof of the result by Burckel and Laver that the standard generators of a braid group are strongly positive. Finally, we discuss relations between the right invariant order and quasipositivity. 相似文献
7.
We construct a determinantal resolution of singularities for the universal subscheme in
and prove that it is isomorphic to the variety of total pairs
. 相似文献
8.
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
9.
The multidimensional Sparr interpolation method is implemented in the Besov spaces
and the Lizorkin--Triebel spaces
. It is shown that this results in Besov spaces of type
. An interpolation theorem for Besov spaces using weak conditions of the form
is formulated. 相似文献
10.
L. Yu. Cherednikova 《Mathematical Notes》2005,77(5-6):715-725
Suppose that
is a system of continuous subharmonic functions in the unit disk
and
is the class of holomorphic functions f in
such that log|f(z)| ≤ B
f
p
f
(z) + C
f
, z ∈
, where B
f
and C
f
are constants and p
f
∈
. We obtain sufficient conditions for a given number sequence Λ = { λn} ⊂
to be a subsequence of zeros of some nonzero holomorphic function from
, i.e., Λ is a nonuniqueness sequence for
.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 775–787.Original Russian Text Copyright ©2005 by L. Yu. Cherednikova. 相似文献
11.
Quasiconcave functions
and
belong to the same scale if there exist quasiconcave functions
and
and numbers
such that
and
. We establish a criterion for such functions to belong to the same scale up to equivalence. This criterion is obtained in terms of nodes of the corresponding linear-constant step-functions. It turns out that nodes must be equivalent to sequences. 相似文献
12.
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
13.
R. S. Davtyan 《Mathematical Notes》1969,6(4):725-732
It is shown that for convergence of every orthonormal system
n(x) given on [0, l],it is necessary and sufficient that, under the condition
on tlie increasing function W(x) and for
there hold
almost everywhere on [0, 1].Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 451–462, October, 1969. 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.
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
16.
Fairly general conditions on the coefficients
of even and odd trigonometric Fourier series under which L-convergence (boundedness) of partial sums of the series is equivalent to the relation
are given. 相似文献
17.
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
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.
Avishay Vaknin 《K-Theory》2001,24(1):57-68
For a small triangulated category
, Bass's K
1 group
is described, and the theorem of the heart is proved. We define the determinant map from
to Neeman's
, and we compute this map when
is the derived category of an Abelian category
. 相似文献
20.
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