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1.
We prove that the maximal Fej'er operator is not bounded on the real Hardy spaces H
1, which may be considered over
and
. We also draw corollaries for the corresponding Hardy spaces over
2 and
2.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
A point set
is k-convex if there are at most k points of
in any triangle having its vertices in
. Károlyi, Pach and Tóth [6] showed that if a 1-convex set has sufficiently many points, then it contains an arbitrarily large emtpy convex polygon. They also constructed exponentially large 1-convex sets that contain no empty convex n-gons. Here we shall give an exponential upper bound to the number of points needed. Valtr [8] proved a similar result for k-convex sets. In this paper we improve his upper bound and give an elementary proof of the statement. 相似文献
3.
A subsemigroup S of a semigroup Q is a straight left order in Q and Q is a semigroup of straight left quotients of S if every q ∈ Q can be written as
for some
with a
b in Q and if, in addition, every element of S that is square cancellable lies in a subgroup of Q. Here a
♯ denotes the group inverse of a in some (hence any) subgroup of Q. If S is a straight left order in Q, then Q is necessarily regular; the idea is that Q has a better understood structure than that of S. Necessary and sufficient conditions exist on a semigroup S for S to be a straight left order. The technique is to consider a pair
of preorders on S. If such a pair satisfies conditions mimicking those satisfied by
on a regular semigroup, and if certain subsemigroups of S are right reversible, then S is a straight left order. The conditions required for
to satisfy are somewhat lengthy. In this paper we aim to circumvent some of these by specialising in two ways. First we consider
only fully stratified left orders, that is, the case where
(certainly the most natural choice for
) and the other is to insist that S be abundant, that is, every
-class and every
-class of S contains an idempotent.
Our results may be used to show that the monoid of endomorphisms of a hereditary basis algebra of finite rank is a fully stratified
straight left order.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
4.
Let ℂ denote the complex numbers and
denote the ring of complex-valued Laurent polynomial functions on ℂ\{0}. Furthermore, we denote by
the subsets of Laurent polynomials whose restriction to the unit circle is real, nonnegative, respectively. We prove that
for any two Laurent polynomials
, which have no common zeros in ℂ\{0} there exists a pair of Laurent polynomials
satisfying the equation Q
1
P
1 + Q
2
P
2 = 1. We provide some information about the minimal length Laurent polynomials Q
1 and Q
2 with these properties and describe an algorithm to compute them. We apply this result to design a conjugate quadrature filter
whose zeros contain an arbitrary finite subset Λ⊂ℂ\{0} with the property that for every
implies
and
.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
A group G has finite rank r if every finitely generated subgroup of G is at most r-generator. If C is a class of groups then we let C* denote the class of groups G in which every proper subgroup of G is either of finite rank or in C. We let denote the class of soluble groups and the class of soluble groups of derived length at most d, where d is a positive integer. We let λ denote the set of closure operations
and let denote the λ-closure of the class of periodic locally graded groups. Amongst other results we prove that a soluble -group is either of finite rank or of derived length at most d and also that a group in the class is either locally soluble, or has finite rank, or is isomorphic to one of or for suitable locally finite fields .
The second author would like to thank the Department of Mathematics at Bucknell University for its hospitality while part
of this work was being done. 相似文献
6.
Let
denote the unit sphere in
and
the geodesic distance in
. A spherical‐basis function approximant is a function of the form
, where
are real constants,
is a fixed function, and
is a set of distinct points in
. It is known that if
is a strictly positive definite function in
, then the interpolation matrix
is positive definite, hence invertible, for every choice of distinct points
and every positive integer M. The paper studies a salient subclass of such functions
, and provides stability estimates for the associated interpolation matrices.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
7.
Given a unital C*-algebra
and a right C*-module
over
, we consider the problem of finding short smooth curves in the sphere
= {x ∈
: 〈x, x〉 = 1}. Curves in
are measured considering the Finsler metric which consists of the norm of
at each tangent space of
. The initial value problem is solved, for the case when
is a von Neumann algebra and
is selfdual: for any element x
0 ∈
and any tangent vector ν at x
0, there exists a curve γ(t) = e
tZ
(x
0), Z ∈
, Z* = −Z and ∥Z∥ ≤ π, such that γ(0) = x
0 and
(0) = ν, which is minimizing along its path for t ∈ [0, 1]. The existence of such Z is linked to the extension problem of selfadjoint operators. Such minimal curves need not be unique. Also we consider the
boundary value problem: given x
0, x
1 ∈
, find a curve of minimal length which joins them. We give several partial answers to this question. For instance, let us
denote by f
0 the selfadjoint projection I − x
0 ⊗ x
0, if the algebra f
0
f
0 is finite dimensional, then there exists a curve γ joining x
0 and x
1, which is minimizing along its path.
相似文献
8.
ALAIN HÉNAUT 《Geometriae Dedicata》1997,65(1):89-101
A d-web in (
,0) is given by d complex analytic foliations of codimension one in (
,0) which are in general position. A d-web
in (
,0) is linear if all the leaves are (pieces of) hyperplanes in
and
is algebraic if it is associated, by duality, to a nondegenerate algebraic curve in
of degree d. We characterize linear webs in (
,0). We give explicit conditions under which a linear d-web in (
,0) is algebraic and we obtain equations for
in this case. Some related problems are discussed and some questions are posed. 相似文献
9.
10.
Let G be a finite abelian group and S =
a minimal zero-sum sequence in G of maximal length |S| = l. We study the order of the elements
相似文献
11.
Let
be a group of affine transformations of the plane that contains a strict contraction and all translations. It is shown that
any two topological discs
are congruent dissection with respect to
such that only three topological discs are used as pieces of dissection. Two pieces of dissection do not suffice in general
even if
consists of all affine transformations.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
12.
Let X = {X(t),t <σ} (σ is lifespan) be a birth and death process with explosion whose characteristic triple (Mα,MC,MD) of MX in terms of (α, C, D) and M. This means that a lot of given birth and death processes can be embedded in one and the same birth and death process. If κ∈ E and M = {κ},we decompose X into κX, κ∈ E. 相似文献
13.
A subset S of a d-dimensional convex body K is extensive if S
∂K and for any p, q ∈ S the distance between p and q is at least one-half of the maximum length of chords of K parallel to the segment pq. In this paper we establish the general upper bound |S| ≤ 3
d
— 1. We also find an upper bound for a certain class of 3-polytopes, which leads to the determination of the maximum cardinalities
of extensive subsets and their extremal configurations for tetrahedra, octahedra and some other 3-polytopes.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
14.
We prove that for any positive real number
which is not an integer, the density of the integers
which are coprime to
, a result conjectured by Moser, Lambek and Erd Hs.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
Let 0 < c < s be fixed real numbers such that
, and let f : E2 → E
d
for d ≥ 2 be a function such that for every p, q ∈ E
2 if |p − q| = c, then |f(p) − f(q)| ≤ c, and if |p − q| = s, then |f(p) − f(q)| ≥ s. Then f is a congruence. This result depends on and expands a result of Rádo et. al. [9], where a similar result holds, but for
replacing
. We also present a further extensions where E2 is replaced by E
n
for n > 2 and where the range of c/s is enlarged.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
16.
Let M
R
be a faithful multiplication module, where R is a commutative ring. As defined by Anderson,
this ideal has proved to be useful in studying multiplication modules. First of all a cancellation law involving M and the ideals contained in
is proved. Among various applications given, the following result is proved:: There exists a canonical isomorphism
from
onto
such that for any ( Hom R(M,M), x ( M, a ( (M), (xa) = x.(()(a). As an application of this later result it is proved that M is quasi-injective if and only if (M) is quasi-injective. 相似文献
17.
Slowly convergent infinite products
are considered, where
is a sequence of numbers, or a sequence of linear operators. Using an asymptotic expansion for the “remainder” of the infinite
product a method for convergence acceleration is suggested. The method is in the spirit of the d-transformation for series. It is very simple and efficient for some classes of sequences
. For complicated sequences
it involves the solution of some linear systems, but it is still effective.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
18.
Y. Nishimura 《Proceedings of the Steklov Institute of Mathematics》2006,252(1):212-224
For a simple complete multipolytope
in ℝn, Hattori and Masuda defined a locally constant function
on ℝn minus the union of hyperplanes associated with
, which agrees with the density function of an equivariant complex line bundle over a Duistermaat-Heckman measure when
arises from a moment map of a torus manifold. We improve the definition of
and construct a convex chain
on ℝn. The well-definiteness of this convex chain is equivalent to the semicompleteness of the multipolytope
. Generalizations of the Pukhlikov-Khovanskii formula and an Ehrhart polynomial for a simple lattice multipolytope are given
as corollaries. The constructed correspondence ⨑ub;simple semicomplete multipolytopes⫂ub; →; ⨑ub;convex chains⫂ub; is surjective
but not injective. We will study its “kernel.” 相似文献
19.
Consider a regular diffusion process X with finite speed measure m. Denote the normalized speed measure by μ. We prove that the uniform law of large numbers
holds if the class
has an envelope function that is μ-integrable, or if
is bounded in L
p(μ) for some p>1. In contrast with uniform laws of large numbers for i.i.d. random variables, we do not need conditions on the ‘size’ of
the class
in terms of bracketing or covering numbers. The result is a consequence of a number of asymptotic properties of diffusion
local time that we derive. We apply our abstract results to improve consistency results for the local time estimator (LTE)
and to prove consistency for a class of simple M-estimators.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
If H is a Hopf algebra with bijective antipode and α, β ∈ Aut
Hopf
(H), we introduce a category
, generalizing both Yetter-Drinfeld modules and anti-Yetter-Drinfeld modules. We construct a braided T-category
having all the categories
as components, which, if H is finite dimensional, coincides with the representations of a certain quasitriangular T-coalgebra DT(H) that we construct. We also prove that if (α, β) admits a so-called pair in involution, then
is isomorphic to the category of usual Yetter-Drinfeld modules
.
Research partially supported by the programme CERES of the Romanian Ministry of Education and Research, contract no. 4-147/2004. 相似文献