共查询到20条相似文献,搜索用时 46 毫秒
1.
We show that if T:X→X is a continuous linear operator on an F-space X≠{0}, then the set of frequently hypercyclic vectors of T is of first category in X, and this answers a question of A. Bonilla and K.-G. Grosse-Erdmann. We also show that if T:X→X is a bounded linear operator on a Banach space X≠{0} and if T is frequently hypercyclic (or, more generally, syndetically transitive), then the T∗-orbit of every non-zero element of X∗ is bounded away from 0, and in particular T∗ is not hypercyclic. 相似文献
2.
If U,V are closed subspaces of a Fréchet space, then E is the direct sum of U and V if and only if E′ is the algebraic direct sum of the annihilators U° and V°. We provide a simple proof of this (possibly well-known) result. 相似文献
3.
Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are Lipschitz ?-strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
4.
In this paper we connect the well established theory of stochastic differential inclusions with a new theory of set-valued stochastic differential equations. Solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty, bounded, convex and closed subsets of the space L2 consisting of square integrable random vectors. We show that for the solution X to a set-valued stochastic differential equation corresponding to a stochastic differential inclusion, there exists a solution x for this inclusion that is a ‖⋅‖L2-continuous selection of X. This result enables us to draw inferences about the reachable sets of solutions for stochastic differential inclusions, as well as to consider the viability problem for stochastic differential inclusions. 相似文献
5.
Radu Ioan Boţ Ernö Robert Csetnek Gert Wanka 《Nonlinear Analysis: Theory, Methods & Applications》2007
In this paper we give a weaker sufficient condition for the maximal monotonicity of the operator S+A∗TA, where S:X?X∗, T:Y?Y∗ are two maximal monotone operators, A:X→Y is a linear continuous mapping and X,Y are reflexive Banach spaces. We prove that our condition is weaker than the generalized interior-point conditions given so far in the literature. This condition is formulated using the representative functions of the operators involved. In particular, we rediscover some sufficient conditions given in the past using the so-called Fitzpatrick function for the maximal monotonicity of the sum of two maximal monotone operators and for the precomposition of a maximal monotone operator with a linear operator, respectively. 相似文献
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In this paper, we consider a continuous map f:X→X, where X is a compact metric space, and prove that for any positive integer N, f is Schweizer–Smital chaotic if and only if fN is too. 相似文献
8.
Let E be a Banach lattice and F a Banach space. A bounded linear operator T:E→F is an isomorphism on the positive cone of E if and only if T∗ is almost surjective. A dual version of this theorem holds also. A bounded linear operator T:F→E is almost surjective if and only if T∗ is an isomorphism on the positive cone of F∗. 相似文献
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We prove that if for a continuous map f on a compact metric space X, the chain recurrent set, R(f) has more than one chain component, then f does not satisfy the asymptotic average shadowing property. We also show that if a continuous map f on a compact metric space X has the asymptotic average shadowing property and if A is an attractor for f, then A is the single attractor for f and we have A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if M is a compact manifold which is not finite with dimM=2, then the C1 interior of the set of all C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of Ω-stable diffeomorphisms. 相似文献
11.
In this paper, we establish an oscillation estimate of nonnegative harmonic functions for a pure-jump subordinate Brownian motion. The infinitesimal generator of such subordinate Brownian motion is an integro-differential operator. As an application, we give a probabilistic proof of the following form of relative Fatou theorem for such subordinate Brownian motion X in a bounded κ-fat open set; if u is a positive harmonic function with respect to X in a bounded κ-fat open set D and h is a positive harmonic function in D vanishing on Dc, then the non-tangential limit of u/h exists almost everywhere with respect to the Martin-representing measure of h. 相似文献
12.
Let f:X→Y be a morphism between normal complex varieties, where Y is Kawamata log terminal. Given any differential form σ, defined on the smooth locus of Y, we construct a “pull-back form” on X. The pull-back map obtained by this construction is ?Y-linear, uniquely determined by natural universal properties and exists even in cases where the image of f is entirely contained in the singular locus of Y. 相似文献
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The truncated variation, TVc, is a fairly new concept introduced in ?ochowski (2008) [5]. Roughly speaking, given a càdlàg function f, its truncated variation is “the total variation which does not pay attention to small changes of f, below some threshold c>0”. The very basic consequence of such approach is that contrary to the total variation, TVc is always finite. This is appealing to the stochastic analysis where so-far large classes of processes, like semimartingales or diffusions, could not be studied with the total variation. Recently in ?ochowski (2011) [6], another characterization of TVc has been found. Namely TVc is the smallest possible total variation of a function which approximates f uniformly with accuracy c/2. Due to these properties we envisage that TVc might be a useful concept both in the theory and applications of stochastic processes. 相似文献
15.
In this paper, continuity of the set-valued metric generalized inverse T∂ in approximatively compact Banach spaces is investigated by means of the methods of geometry of Banach spaces. Necessary and sufficient conditions for upper semicontinuity (continuity) for the set-valued metric generalized inverses T∂ are given. Moreover, authors also prove that if X is a nearly dentable space and H is a hyperplane of X, then H is approximatively compact iff PH(x) is compact for any x∈X. 相似文献
16.
We study the error induced by the time discretization of decoupled forward–backward stochastic differential equations (X,Y,Z). The forward component X is the solution of a Brownian stochastic differential equation and is approximated by a Euler scheme XN with N time steps. The backward component is approximated by a backward scheme. Firstly, we prove that the errors (YN−Y,ZN−Z) measured in the strong Lp-sense (p≥1) are of order N−1/2 (this generalizes the results by Zhang [J. Zhang, A numerical scheme for BSDEs, The Annals of Applied Probability 14 (1) (2004) 459–488]). Secondly, an error expansion is derived: surprisingly, the first term is proportional to XN−X while residual terms are of order N−1. 相似文献
17.
We consider N independent stochastic processes (Xj(t),t∈[0,T]), j=1,…,N, defined by a one-dimensional stochastic differential equation with coefficients depending on a random variable ?j and study the nonparametric estimation of the density of the random effect ?j in two kinds of mixed models. A multiplicative random effect and an additive random effect are successively considered. In each case, we build kernel and deconvolution estimators and study their L2-risk. Asymptotic properties are evaluated as N tends to infinity for fixed T or for T=T(N) tending to infinity with N. For T(N)=N2, adaptive estimators are built. Estimators are implemented on simulated data for several examples. 相似文献
18.
Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are bounded strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. A new explicit coupled iteration process is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
19.
In this paper, we prove a kind of Abelian theorem for a class of stochastic volatility models (X,V) where both the state process X and the volatility process V may have jumps. Our results relate the asymptotic behavior of the characteristic function of XΔ for some Δ>0 in a stationary regime to the Blumenthal–Getoor indexes of the Lévy processes driving the jumps in X and V. The results obtained are used to construct consistent estimators for the above Blumenthal–Getoor indexes based on low-frequency observations of the state process X. We derive convergence rates for the corresponding estimator and show that these rates cannot be improved in general. 相似文献
20.
For a non-degenerate convex subset Y of the n -dimensional Euclidean space Rn, let F(Y) be the family of all fuzzy sets of Rn which are upper semicontinuous, fuzzy convex and normal with compact supports contained in Y . We show that the space F(Y) with the topology of sendograph metric is homeomorphic to the separable Hilbert space ?2 if Y is compact; and the space F(Rn) is also homeomorphic to ?2. 相似文献