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1.
It is proved that faces of the unit spheres of the mass and comass norms are totally geodesic submanifolds in the manifolds of the extreme points of the spheres. A canonical embedding of the complex projective space
in the Plücker model of the Grassmannian
is described, and some of the properties of the embedding are proved. As an application of these results, the 2-dimensional sections in
having minimal curvature are characterized geometrically. Bibliography: 16 titles. 相似文献
2.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
3.
Let
be a continuous semimartingale and let
be a continuous function of bounded variation. Setting
and
suppose that a continuous function
is given such that F is C1,2 on
and F is
on
. Then the following change-of-variable formula holds:
where
is the local time of X at the curve b given by
and
refers to the integration with respect to
. A version of the same formula derived for an Itô diffusion X under weaker conditions on F has found applications in free-boundary problems of optimal stopping. 相似文献
4.
A canonical bijection between the set of extreme points of the comass-unit sphere
and the manifold of orthogonal complex structures in
is described, under which unitary bases correspond to decompositions of the forms realizing the conjugate norm of the mass. This correspondence is used for obtaining a classification of faces of the sphere
and the known classification of faces of the set polar to
. Bibliography: 10 titles. 相似文献
5.
In this paper, we give an Lp-Lq-version of Morgans theorem for the Dunkl-Bessel transform
on
More precisely, we prove that for all
and
then for all measurable function f on
the conditions
and
imply f = 0, if and only if
where
are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004 相似文献
6.
P. V. Stetlov 《Journal of Mathematical Sciences》2001,104(4):1399-1409
Any link in
is isotopic to a knot lying on the polyhedron
. A nontrivial theory of links and knots on T is developed. The main result is a construction of an isotopy invariant, which can distinguish pairs of knots on T that are isotopic as knots in
. Bibliography: 3 titles. 相似文献
7.
Roland Duduchava 《Integral Equations and Operator Theory》1992,15(3):412-426
Conditions on the kernel of the classical Wiener-Hopf equation are obtained which provide the same smoothness of any solution in terms of its inclusion in different spaces of smooth functions such as
as the function in the right side of the equation. 相似文献
9.
Let
denote the closed subspace of
consisting of analytic functions in the unit disk
. For certain class of subharmonic
, the Hankel operatorH
b on
with symbol
is studied. Criteria for boundedness and compactness of such kind of Hankel operators are presented.R. Rochberg's research was partially supported by a grant from the National Science Foundation. 相似文献
10.
11.
In this paper, the boundedness of the Riesz potential generated by generalized shift operator
from the spaces
to the spaces
is examined. 相似文献
12.
M. Yu. Zvagel'skii 《Journal of Mathematical Sciences》2001,104(4):1276-1282
We single out the obstruction for a closed
-null-homologous submanifold of codimension 2 to be the boundary of a submanifold of codimension 1. As an application, we calculate the groups
of cobordisms of embeddings of nonoriented n-manifolds in the Euclidean (n+2)-space for n=3 and 4. Namely, we show that
and
. A specific generator of the former group is explicitly given. Bibliography: 5 titles. 相似文献
13.
The solutions of the equation
in
, where
are investigated,
Bessel potentials of higher order are defined, and recurrence relations
between these solutions and these Bessel potentials are obtained. It is
also proved that these solutions and the solutions of
, under certain conditions, are identical.
Received: 6 November 2002 相似文献
14.
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
15.
P. M. G. Manchón 《Czechoslovak Mathematical Journal》2002,52(1):1-9
In this paper we study the hypersurfaces
given as connected compact regular fibers of a differentiable map
, in the cases in which
has finitely many nondegenerate critical points in the unbounded component of
. 相似文献
16.
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
17.
Boundary properties of first-order partial derivatives of the Poisson integral are studied in the half-space
. 相似文献
18.
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
19.
In the six-dimensional space
of bivectors, a Lie product similar to the standard vector product in
is introduced. The Lie algebra constructed is proved to be isomorphic to the Lie algebra of the orthogonal group
, and the isomorphism is a canonical isometry between
and the space of antisymmetric operators in
. Bibliography: 2 titles. 相似文献
20.
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