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1.
Let T be a Banach space operator, E(T) be the set of all isolated eigenvalues of T and π(T) be the set of all poles of T. In this work, we show that Browder's theorem for T is equivalent to the localized single-valued extension property at all complex numbers λ in the complement of the Weyl spectrum of T, and we give some characterization of Weyl's theorem for operator satisfying E(T) = π(T). An application is also given. 相似文献
2.
Stephan Hell 《Discrete and Computational Geometry》2008,40(4):586-594
Birch and Tverberg partitions are closely related concepts from discrete geometry. We show two properties for the number of
Birch partitions: Evenness and a lower bound. This implies the first nontrivial lower bound for the number of Tverberg partitions
that holds for arbitrary q, where q is the number of partition blocks. The proofs are based on direct arguments and do not use the equivariant method from topological
combinatorics. 相似文献
3.
We prove Kantorovich’s theorem on Newton’s method using a convergence analysis which makes clear, with respect to Newton’s
method, the relationship of the majorant function and the non-linear operator under consideration. This approach enables us
to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate and to obtain a new estimate of this rate based on a directional derivative of the derivative of the majorant function. Moreover, the majorant function does not have to be defined beyond its first root for obtaining
convergence rate results.
The research of O.P. Ferreira was supported in part by FUNAPE/UFG, CNPq Grant 475647/2006-8, CNPq Grant 302618/2005-8, PRONEX–Optimization(FAPERJ/CNPq)
and IMPA.
The research of B.F. Svaiter was supported in part by CNPq Grant 301200/93-9(RN) and by PRONEX–Optimization(FAPERJ/CNPq). 相似文献
4.
Yingchun CAI 《数学年刊B辑(英文版)》2008,29(6):687-698
Let p denote a prime and P2 denote an almost prime with at most two prime factors. The author proves that for sufficiently large x,∑p≤x p+2=P2 1〉1.13Cx/log^2x,where the constant 1.13 constitutes an improvement of the previous result 1.104 due to J. Wu. 相似文献
5.
J. Ruppenthal 《Journal of Geometric Analysis》2008,18(4):1127-1132
Let X be a connected normal Stein space of pure dimension d≥2 with finitely many isolated singularities. By solving a weighted
-equation with compact support on a desingularization of X, we derive Hartogs’ Extension Theorem on X by the
-idea due to Ehrenpreis.
相似文献
6.
Letf be a continuous function on the unit circle Γ, whose Fourier series is ω-absolutely convergent for some weight ω on the set
of integersZ. If f is nowhere vanishing on Γ, then there exists a weightv onZ such that 1/f hadv-absolutely convergent Fourier series. This includes Wiener’s classical theorem. As a corollary, it follows that if φ is holomorphic
on a neighbourhood of the range off, then there exists a weight Χ on Z such that φ ◯f has Χ-absolutely convergent Fourier series. This is a weighted analogue of Lévy’s generalization of Wiener’s theorem. In
the theorems,v and Χ are non-constant if and only if ω is non-constant. In general, the results fail ifv or Χ is required to be the same weight ω. 相似文献
7.
R. N. Karasev 《Discrete and Computational Geometry》2008,39(4):766-777
In this paper, we consider finite families of convex sets in ℝ
d
such that every d or fewer sets of the family have a common point. For some families of this type, we give upper bounds on the size of a finite
set intersecting all sets of the family.
This research was supported by the Russian Foundation for the Basic Research Grants No. 03-01-00801 and 06-01-00648, and by
the President of the Russian Federation Grant No. MK-5724.2006.1. 相似文献
8.
In this paper we consider abstract equations of the typeK
ν
ν +ν =w
0, in a closed convex subset of a separable Hilbert spaceH. For eachv in the closed convex subset,K
v :H →H is a bounded linear map. As an application of our abstract result we obtain an existence result for nonlinear integral equations
of the typeν(s)+ν(s)∫
0
1
k(s,t)ν(t)dt =W
0(s) in the spaceL
2 [0,1]. 相似文献
9.
On the Equivalence and Generalized of Weyl Theorem Weyl Theorem 总被引:3,自引:0,他引:3
M. BERKANI 《数学学报(英文版)》2007,23(1):103-110
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a sinlilar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators. 相似文献
10.
If T or T* is an algebraically quasi-class A operator acting on an infinite dimensional separable Hilbert space then we prove that
Weyl’s theorem holds for f(T) for every f ∈ H(σ(T)), where H(σ(T)) denotes the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is algebraically quasi-class A then a-Weyl’s theorem holds for f(T). Also, if T or T* is an algebraically quasi-class A operator then we establish that the spectral mapping theorems for the Weyl spectrum and
the essential approximate point spectrum of T for every f ∈ H(σ(T)), respectively.
This research was supported by the Kyung Hee University Research Fund in 2007 (KHU- 20071605). 相似文献
11.
Let m(n) be the maximum integer such that every partially ordered set P with n elements contains two disjoint subsets A and B, each with cardinality m(n), such that either every element of A is greater than every element of B or every element of A is incomparable with every element of B. We prove that . Moreover, for fixed ε ∈ (0,1) and n sufficiently large, we construct a partially ordered set P with n elements such that no element of P is comparable with other elements of P and for every two disjoint subsets A and B of P each with cardinality at least , there is an element of A that is comparable with an element of B. 相似文献
12.
Yanxun Chang 《数学学报(英文版)》2000,16(1):103-112
Abstract
Given any positive integers k≥ 3 and λ, let c(k, λ) denote the smallest integer such that v∈B(k, λ) for every integer v≥c(k, λ) that satisfies the congruences λv(v− 1) ≡ 0(mod k(k− 1)) and λ(v− 1) ≡ 0(mod k− 1). In this article we make an improvement on the bound of c(k, λ) provided by Chang in [4] and prove that
. In particular,
.
Supported by NSFC Grant No. 19701002 and Huo Yingdong Foundation 相似文献
13.
Let r
1, …, r
s
be non-zero integers satisfying r
1 + ⋯ + r
s
= 0. Let G be a finite abelian group with k
i
|k
i-1(2 ≤ i ≤ n), and suppose that (r
i
, k
1) = 1(1 ≤ i ≤ s). Let denote the maximal cardinality of a set which contains no non-trivial solution of r
1
x
1 + ⋯ + r
s
x
s
= 0 with . We prove that . We also apply this result to study problems in finite projective spaces.
相似文献
14.
Songliang Qiu 《中国科学A辑(英文版)》1998,41(12):1241-1247
Some properties and asymptotically sharp bounds are obtained for singdar values of Ramanujan’s generalized modular equation.
from which infinite-product representations of the Hersch-Pfluger ϕdimtortion function ϕ
K
(r) and the Agard η-distortion function η
K
(t) follow. By these results, the explicit quasiconformal Schwan lemma is improved, several properties are obtained for the
Schottky upper bound, and a conjecture on the linear distortion function λ (K) is proved to be true. 相似文献
15.
Sergiy Maksymenko 《Central European Journal of Mathematics》2009,7(2):272-298
Let F be a C
∞ vector field defined near the origin O ∈ ℝ
n
, F(O) = 0, and (F
t
) be its local flow. Denote by
the set of germs of orbit preserving diffeomorphisms h: ℝ
n
→ ℝ
n
at O, and let
, (r ≥ 0), be the identity component of
with respect to the weak Whitney W
r
topology. Then
contains a subset
consisting of maps of the form F
α(x)(x), where α: ℝ
n
→ ℝ runs over the space of all smooth germs at O. It was proved earlier by the author that if F is a linear vector field, then
=
.
In this paper we present a class of examples of vector fields with degenerate singularities at O for which
formally coincides with
, i.e. on the level of ∞-jets at O.
We also establish parameter rigidity of linear vector fields and “reduced” Hamiltonian vector fields of real homogeneous polynomials
in two variables.
相似文献
16.
Xiao Hong CAO 《数学学报(英文版)》2007,23(5):951-960
Two variants of the essential approximate point spectrum are discussed. We find for example that if one of them coincides with the left Drazin spectrum then the generalized a-Weyl's theorem holds, and conversely for a-isoloid operators. We also study the generalized a-Weyl's theorem for Class A operators. 相似文献
17.
Let (V, g) be a Riemannian manifold and let be the isometric immersion operator which, to a map , associates the induced metric on V, where denotes the Euclidean scalar product in . By Nash–Gromov implicit function theorem is infinitesimally invertible over the space of free maps. In this paper we study non-free isometric immersions . We show that the operator (where denotes the space of C
∞- smooth quadratic forms on ) is infinitesimally invertible over a non-empty open subset of and therefore is an open map in the respective fine topologies.
相似文献
18.
Micha A. Perles Horst Martini Yaakov S. Kupitz 《Discrete and Computational Geometry》2009,42(2):277-304
The Jordan Curve Theorem referring to a simple closed curve in the plane has a particularly simple proof in the case that
the curve is polygonal, called the “raindrop proof”. We generalize the notion of a simple closed polygon to that of a polyhedral
(d−1)-pseudomanifold (d≥2) and prove a Jordan–Brouwer Separation Theorem for such a manifold embedded in ℝ
d
. As a by-product, we get bounds on the polygonal diameter of the interior and exterior of such a manifold which are almost
tight. This puts the result within the frame of computational geometry.
The research of Y.S. Kupitz was partially supported by the Landau Center at the Mathematics Institute of the Hebrew University
of Jerusalem (supported by Minerva Foundation, Germany), and by Deutsche Forschungsgemeinschaft. 相似文献
19.
Xiaoping Yuan 《中国科学A辑(英文版)》1998,41(6):595-605
The boundedness of all solutions is shown for Duffing-type equations
wherep
1,p
2,...,p
2n are of period 1 and of Lipschitzian continuity andp
n+1,...,p
2n are of Zygmundian continuity. This conclusion implies that the boundedness phenomenon for the Duffing-type equations does
not require the smoothness in the time-variable, thus answering the question posed by Dieckerhoff and Zehnder. 相似文献
20.
LetN be a sufficiently large even integer and
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