共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove a generalized implicit function theorem for Banach spaces, without the usual assumption that the subspaces involved
being complemented. Then we apply it to the problem of parametrization of fibers of differentiable maps, the Lie subgroup
problem for Banach–Lie groups, as well as Weil’s local rigidity for homomorphisms from finitely generated groups to Banach–Lie
groups.
相似文献
2.
Patrick J. Rabier 《Journal of Mathematical Analysis and Applications》2004,290(1):171-189
We give a new form of the Ascoli theorem for functions on tending to some given closed subset Z of a complete metric space E at infinity. For instance, when E is a normed space and Z={0}, the usual uniform decay requirement is replaced by the assumption that the 0 function is the only continuous function produced by some limiting process. This formulation, which has significant practical value in concrete applications, is described in its general form, but with emphasis on the case when Z is totally disconnected. Variants in Sobolev spaces and the properness of nonlinear ordinary differential operators are discussed. 相似文献
3.
Janusz Matkowski 《Journal of Mathematical Analysis and Applications》2011,373(1):227-234
For a function f defined in an interval I, satisfying the conditions ensuring the existence and uniqueness of the Lagrange mean L[f], we prove that there exists a unique two variable mean M[f] such that
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5.
Satoshi Suzuki Daishi Kuroiwa 《Journal of Mathematical Analysis and Applications》2011,379(2):649-655
In convex programming, sandwich theorem is very important because it is equivalent to Fenchel duality theorem. In this paper, we investigate a sandwich theorem for quasiconvex functions. Also, we consider some applications for quasiconvex programming. 相似文献
6.
Luis J. Alías Marcos Dajczer Jaime Ripoll 《Annals of Global Analysis and Geometry》2007,31(4):363-373
The classical Bernstein theorem asserts that any complete minimal surface in Euclidean space
that can be written as the graph of a function on
must be a plane. In this paper, we extend Bernstein’s result to complete minimal surfaces in (may be non-complete) ambient
spaces of non-negative Ricci curvature carrying a Killing field. This is done under the assumption that the sign of the angle
function between a global Gauss map and the Killing field remains unchanged along the surface. In fact, our main result only
requires the presence of a homothetic Killing field.
L.J. Alías was partially supported by MEC/FEDER project MTM2004-04934-C04-02, F. Séneca project 00625/PI/04, and F. Séneca
grant 01798/EE/05, Spain 相似文献
7.
Mark Holland Stefano Luzzatto § 《Journal of Difference Equations and Applications》2013,19(6):535-551
We introduce a new technique for proving the classical stable manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the convergence of a canonical sequence of “finite time local stable manifolds” which are related to the dynamics of a finite number of iterations. 相似文献
8.
We prove the generalized Obata theorem on foliations. Let M be a complete Riemannian manifold with a foliation F of codimension q?2 and a bundle-like metric gM. Then (M,F) is transversally isometric to (Sq(1/c),G), where Sq(1/c) is the q-sphere of radius 1/c in (q+1)-dimensional Euclidean space and G is a discrete subgroup of the orthogonal group O(q), if and only if there exists a non-constant basic function f such that for all basic normal vector fields X, where c is a positive constant and ∇ is the connection on the normal bundle. By the generalized Obata theorem, we classify such manifolds which admit transversal non-isometric conformal fields. 相似文献
9.
Mitsuhiro Itoh Jun Masamune Takanari Saotome 《Proceedings of the American Mathematical Society》2008,136(10):3539-3548
It is proved that the Hodge decomposition and Serre duality hold on a non-compact weighted CR manifold with negligible boundary. A complete CR manifold has negligible boundary. Some examples of complete CR manifolds are presented.
10.
Maki Nakasuji 《Transactions of the American Mathematical Society》2006,358(8):3285-3303
For a -dimensional hyperbolic manifold , we consider an estimate of the error term of the prime geodesic theorem. Put the fundamental group of to be a discrete subgroup of with cofinite volume. When the contribution of the discrete spectrum of the Laplace-Beltrami operator is larger than that of the continuous spectrum in Weyl's law, we obtained a lower estimate as goes to .
11.
Marios Mavronicolas 《Discrete Mathematics》2009,309(12):3757-3766
A graceful labeling of a graph G=(V,E) assigns |V| distinct integers from the set {0,…,|E|} to the vertices of G so that the absolute values of their differences on the |E| edges of G constitute the set {1,…,|E|}. A graph is graceful if it admits a graceful labeling. The forty-year old Graceful Tree Conjecture, due to Ringel and Kotzig, states that every tree is graceful.We prove a Substitution Theorem for graceful trees, which enables the construction of a larger graceful tree through combining smaller and not necessarily identical graceful trees. We present applications of the Substitution Theorem, which generalize earlier constructions combining smaller trees. 相似文献
12.
For a family of weight functions invariant under a finite reflection group, we show how weighted Lp multiplier theorems for Dunkl transform on the Euclidean space Rd can be transferred from the corresponding results for h-harmonic expansions on the unit sphere Sd of Rd+1. The result is then applied to establish a Hörmander type multiplier theorem for the Dunkl transform and to show the convergence of the Bochner-Riesz means of the Dunkl transform of order above the critical index in weighted Lp spaces. 相似文献
13.
A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature. 相似文献
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15.
An automatic adjoint theorem and its applications 总被引:2,自引:0,他引:2
In this paper, we prove the following automatic adjoint theorem: For any sequence spaces and , if has the signed-weak gliding hump property and is an infinite matrix which transforms into , then the transpose matrix of transforms into , and for any and , . That is, the adjoint operator of automatically exists and is just the transpose matrix of . From the theorem we obtain a class of infinite matrix topological algebras , and prove also a -multiplier convergence theorem of Orlicz-Pettis type. The theorem improves substantially the famous Stiles' Orlicz-Pettis theorem.
16.
The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability results concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented. 相似文献
17.
Geometric structure of the joint N‐voM distribution manifold and its applications to sensor networks 下载免费PDF全文
In this paper, the geometric structure for normal distribution manifold, von Mises distribution manifold and their joint distribution manifold are firstly given by the metric, curvature, and divergence, respectively. Furthermore, the active detection with sensor networks is presented by a classical measurement model based on metric manifold, and the information resolution is presented for the range and angle measurements sensor networks. The preliminary analysis results introduced in this paper indicate that our approach is able to offer consistent and more comprehensive means to understand and solve sensor network problems containing sensors management and target detection, which are not easy to be handled by conventional analysis methods. 相似文献
18.
I present an inverse function theorem for differentiable maps between Fréchet spaces which contains the classical theorem of Nash and Moser as a particular case. In contrast to the latter, the proof does not rely on the Newton iteration procedure, but on Lebesgue's dominated convergence theorem and Ekeland's variational principle. As a consequence, the assumptions are substantially weakened: the map F to be inverted is not required to be C2, or even C1, or even Fréchet-differentiable. 相似文献
19.
In this paper, we first give a simple proof of the decomposition theorem in Alber (Field Inst. Comm. 25 (2000) 77) and then present a new decomposition of arbitrary elements in reflexive strictly convex and smooth Banach spaces. As applications of the decomposition theorem, we give the representations of the metric projection operator for some kind of closed convex sets. Finally, we provide a sufficient condition under which the generalized projection operator coincides with the metric projection operator. 相似文献
20.
Zbigniew Blocki 《中国科学A辑(英文版)》2005,48(Z1)
We show that the uniform estimate in the Calabi-Yau theorem easily follows from the local stability of the complex Monge-Ampere equation. 相似文献