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Let , B and Aj () be real nonsingular n×n matrices, λk () be real numbers. In this paper we present a sufficient condition for the system to be a frame for . This sufficient condition also shows the stability of the system with respect to the perturbation of matrix dilation parameters and the perturbation of translation parameters . 相似文献
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In this paper, we develop a stochastic calculus related to a fractional Brownian sheet as in the case of the standard Brownian sheet. Let be a fractional Brownian sheet with Hurst parameters H=(H1,H2), and (2[0,1],B(2[0,1]),μ) a measure space. By using the techniques of stochastic calculus of variations, we introduce stochastic line integrals along all sufficiently smooth curves γ in 2[0,1], and four types of stochastic surface integrals: , i=1,2, , , , . As an application of these stochastic integrals, we prove an Itô formula for fractional Brownian sheet with Hurst parameters H1,H2∈(1/4,1). Our proof is based on the repeated applications of Itô formula for one-parameter Gaussian process. 相似文献
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Liangping Jiang 《Journal of Mathematical Analysis and Applications》2007,326(2):1379-1382
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a function V(t,x), a(‖x‖)?V(t,x)?b(‖x‖) for some a,b∈K, such that for some c∈K. In this paper we prove that if f(t,x) is bounded, is uniformly continuous and bounded, then the condition that can be weakened and replaced by and contains no complete trajectory of , t∈[−T,T], where , uniformly for (t,x)∈[−T,T]×BH. 相似文献
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On commutators of Marcinkiewicz integrals with rough kernel 总被引:2,自引:0,他引:2
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Wolfgang Knirsch Georg Schneider 《Journal of Mathematical Analysis and Applications》2006,320(1):403-414
In this paper we investigate Hankel operators with anti-holomorphic symbols ∈L2(C,m|z|), where are general Fock spaces. We will show that is not continuous if the corresponding symbol is not a polynomial . For polynomial symbols we will give necessary and sufficient conditions for continuity and compactness in terms of N and m. For monomials we will give a complete characterization of the Schatten-von Neumann p-class membership for p>0. Namely in case 2k<m the Hankel operators are in the Schatten-von Neumann p-class iff p>2m/(m−2k); and in case 2k?m they are not in the Schatten-von Neumann p-class. 相似文献
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Gen-Qi Xu 《Journal of Mathematical Analysis and Applications》2004,289(2):493-504
The eventually norm continuous semigroups on Hilbert space and perturbation are studied in this paper. By resolvent of infinitesimal generator, the sufficient and necessary conditions for eventually norm continuous semigroups are given. Using the result obtained, it is proved that if is infinitesimal generator of an eventually norm continuous semigroup T(t), then there is a subspace ΞA of such that, for any , the semigroup S(t) generated by preserves the property of T(t). 相似文献
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Let C be a closed convex subset of a uniformly smooth Banach space E and let T:C→C be a nonexpansive mapping with a nonempty fixed points set. Given a point u∈C, the initial guess x0∈C is chosen arbitrarily and given sequences , and in (0,1), the following conditions are satisfied:
- (i)
- ;
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- αn→0, βn→0 and 0<a?γn, for some a∈(0,1);
- (iii)
- , and . Let be a composite iteration process defined by
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Yasuo Komori 《Journal of Mathematical Analysis and Applications》2003,286(1):80-88
We consider the boundedness of Calderón-Zygmund operators from to , where is the Hardy space associated with the Herz space and is the local version of . We show Calderón's commutator is bounded from to . 相似文献
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In this paper, we show that if is an n-dimensional subspace of L(V) such that every nonzero transformation of has rank greater than or equal to 2n−1 then is algebraically reflexive. If is an n-dimensional subspace of B(H) such that every nonzero transformation of has rank greater than or equal to 2n−1 then is hyperreflexive. We also consider how to construct some new hyperreflexive subspaces. 相似文献
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Liangping Jiang 《Journal of Mathematical Analysis and Applications》2005,301(2):378-383
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a positive definite function V which has infinitesimal upper bound such that is negative definite. In this paper we prove that if is bounded then the condition that is negative definite can be weakened and replaced by that and is negative definite. 相似文献
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Mitsuru Uchiyama 《Journal of Functional Analysis》2006,231(1):221-244
Let P+ be the set of all non-negative operator monotone functions defined on [0,∞), and put . Then and . For a function and a strictly increasing function h we write if is operator monotone. If and and if and , then . We will apply this result to polynomials and operator inequalities. Let and be non-increasing sequences, and put for t≧a1 and for t≧b1. Then v+?u+ if m≦n and : in particular, for a sequence of orthonormal polynomials, (pn-1)+?(pn)+. Suppose 0<r,p and s=0 or 1≦s≦1+p/r. Then 0≦A≦B implies for 0<α≦r/(p+r). 相似文献
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Zhijun Zhang 《Journal of Mathematical Analysis and Applications》2005,308(2):532-540
By constructing the comparison functions and the perturbed method, it is showed that any solution u∈C2(Ω) to the semilinear elliptic problems Δu=k(x)g(u), x∈Ω, u|∂Ω=+∞ satisfies , where Ω is a bounded domain with smooth boundary in RN; , −2<σ, c0>0, ; g∈C1[0,∞), g?0 and is increasing on (0,∞), there exists ρ>0 such that , ∀ξ>0, , . 相似文献
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C.E. Chidume 《Journal of Mathematical Analysis and Applications》2007,326(2):960-973
Let E be a real uniformly convex Banach space, K be a closed convex nonempty subset of E which is also a nonexpansive retract with retraction P. Let be asymptotically nonexpansive mappings of K into E with sequences (respectively) satisfying kin→1 as n→∞, i=1,2,…,m, and . Let be a sequence in [?,1−?],?∈(0,1), for each i∈{1,2,…,m} (respectively). Let {xn} be a sequence generated for m?2 by
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Dong Joo Moon Seoung Dal Jung 《Journal of Mathematical Analysis and Applications》2008,342(1):354-360
Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that at all x∈M and at some point x0∈M, where μ0>0 is the least eigenvalue of the Laplacian acting on L2-functions on M. Let 2?q?p. Then any q-harmonic map of finite q-energy is constant. Moreover, if N is a Riemannian manifold of non-positive scalar curvature, then any q-harmonic morphism of finite q-energy is constant. 相似文献