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1.
We study two questions posed by Johnson, Lindenstrauss, Preiss, and
Schechtman, concerning the structure of level sets of uniform and Lipschitz
quotient mappings from
. We show that if
, is a uniform quotient mapping then for every
has
a bounded number of components, each component of
separates
and the upper bound of the number of components depends
only on
and the moduli of co-uniform and uniform continuity of
.Next we prove that all level sets of any co-Lipschitz uniformly
continuous mapping from
to
are locally connected, and we show
that for every pair of a constant
and a function
with
, there exists a natural number
, so that
for every co-Lipschitz uniformly continuous map
with a
co-Lipschitz constant
and a modulus of uniform continuity
, there
exists a natural number
and a finite set
with
card
so that for all
has exactly
components,
has exactly
components and
each component of
is homeomorphic with the real line and
separates the plane into exactly 2 components. The number and form
of components of
for
are also described - they have a
finite tree structure. 相似文献
2.
3.
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
4.
Estimates of Marcinkiewicz Integrals with Bounded Homogeneous Kernels of Degree Zero 总被引:2,自引:0,他引:2
Under the cancellation property and a certain Dini-type condition
on kernels, we prove that Marcinkiewicz integrals with kernels which are homogeneous
functions of degree zero, are bounded from
to
,
from
to
, and from
to
for
. 相似文献
5.
For a class of stable planes we define a notion of isotopy equivalence with
respect to that class and prove that any two planes of a certain class of
-planes comprising all affine
-planes are isotopy equivalent. Furthermore we obtain that all affine
-planes are isotopy equivalent in the class of affine
-planes. Finally we give an example which shows that this approach cannot be easily generalized
to 2-dimensional projective planes, and we outline a different way for a
possible generalization.Received: 27 April 2001 相似文献
6.
Let ∑ be either an oriented hyperplane or the unit sphere in
, let
be open and connected and let
be an open and connected domain in
such that
. If in
is a null solution of the Dirac operator (also called a monogenic function in
) which is continuously extendable to
, then conditions upon
are given enabling the monogenic extension of
across
. In such a way Schwarz reflection type principles for monogenic functions are established in the Spin (1) and Spin
cases. The Spin (1) case includes the classical Schwarz reflection principle for holomorphic functions in the plane. The
Spin
case deals with so-called “half boundary value problems” for the Dirac operator.
Received: 2 February 2006 相似文献
8.
We investigate the ideal structure of the Toeplitz algebra
of a totally ordered abelian group
. We show that the primitive ideals of
are parametrised by the disjoint union
of the duals
of the order ideals
of
, and identify the
hull-kernel topology on
when the chain of orderideals in
is isomorphic to a subset of
相似文献
9.
We prove that a finite group G is
-constrained if and only if it contains a nilpotent subgroup
I satisfying
for all
.Received: 22 July 2002 相似文献
10.
We consider the three-dimensional Schrödinger operators
and
where
, A is a magnetic potential generating a constant magnetic
field of strength
, and
where
decays fast enough at infinity. Then, A. Pushnitskis representation of the spectral shift function (SSF)
for the pair of operators
is well defined for energies
We study the behaviour of the associated representative of the equivalence class
determined by the SSF, in a neighbourhood of the Landau levels
Reducing our analysis to the study of the eigenvalue asymptotics for a family of
compact operators of Toeplitz type, we establish a relation between the type of the
singularities of the SSF at the Landau levels and the decay rate of V at infinity.
Communicated by Bernard HelfferSubmitted 23/09/03, accepted 15/01/04 相似文献
11.
In this paper we show that, given a complete lattice
, the following three
lattices are the same: (1) the lattice of closure relations on
, (2) the lattice of meet-closed subsets of
, and (3) the lattice of complete join congruence relations on
. 相似文献
12.
Let
be a C*-algebra and X a Hilbert C*
-module. If
is a projection, let
be the p-sphere of X. For φ a state of
with support p in
and
consider the modular vector state φx of
given by
The spheres
provide fibrations
and
These fibrations enable us to examine the homotopy type of the sets of modular vector states, and relate it to the homotopy type of unitary groups and spaces of projections. We regard modular vector states as generalizations of pure states to the context of Hilbert C*-modules, and the above fibrations as generalizations of the projective fibration of a Hilbert space. 相似文献
13.
Adimurthi K. Sandeep 《NoDEA : Nonlinear Differential Equations and Applications》2007,13(5-6):585-603
Let Ω be a bounded domain in
, we prove the singular Moser-Trudinger embedding:
if and only if
where
and
. We will also study the corresponding critical exponent problem. 相似文献
14.
Dietmar Vogt 《Archiv der Mathematik》2006,87(2):163-171
It is shown that for open convex
, d > 1 and a nontrivial polynomial P the space
does not have property
. If P is elliptic or homogeneous, then this holds for every open Ω. For
even
cannot occur and if it occurs for some Ω, then P must be hypoelliptic.
Received: 18 July 2005 相似文献
15.
Proof of the Ergodic Hypothesis
for Typical Hard Ball Systems 总被引:3,自引:0,他引:3
We consider the system of
hard balls with masses
and radius r in the flat torus
of size
. We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost
every selection
of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the
case
. The method of that proof was primarily dynamical-geometric, whereas
the present approach is inherently algebraic.
Communicated by Eduard ZehnderSubmitted 17/10/02, accepted 01/12/03 相似文献
16.
Niels Jakob Laustsen 《K-Theory》2001,23(2):115-127
We prove that the K-groups of the Banach algebra
of bounded, linear operators on the pth James space
, where 1 < p < , are given by
and
. Moreover, for each Banach space
and each non-zero, closed ideal
contained in the ideal of inessential operators, we show that
and
. This enables us to calculate the K-groups of
for each Banach space
which is a direct sum of finitely many James spaces and
-spaces. 相似文献
17.
In this work we determine the group of modular automorphisms of the
Drinfeld modular curve
for any nonconstant polynomial
.Received: 19 September 2002 相似文献
18.
Let
be a family of holomorphic functions in the unit disk
,
which are also holomorphic in a parameter
. We express
cyclicity (=generalized multiplicity) of a zero of
at
via
some algebraic characteristics of the ideal generated by the Taylor
coefficients of
. As an example we estimate the cyclicity of the
family of generalized exponential polynomials. 相似文献
20.
Let
and
be Hausdorff topological vector spaces over the field
, let
be a bilinear functional, and let
be a non-empty subset of
. Given a set-valued map
and two set-valued maps
, the generalized bi-quasi-variational inequality (GBQVI) problem is to find a point
and a point
such that
and
for all
and for all
or to find a point
a point
and a point
such that
and
for all
. The generalized bi-quasi-variational inequality was introduced first by Shih and Tan [8] in 1989. In this paper we shall obtain some existence theorems of generalized bi-quasi-variational inequalities as application of upper hemi-continuous operators [4] in locally convex topological vector spaces on compact sets. 相似文献