APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.     

SOME RESULTS ON CONTROLLED FRAMES IN HILBERT SPACES

We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds.We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames.We introduce a new perturbation of controlled frames to obtain new frames from a given one.Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.     

EQUIVARIANT COHOMOLOGY AND REPRESENTATIONS OF THE SYMMETRIC GROUP

51. IntroductionIn a recent paper [l], I have shown how to construct a continuous mapf: Cn(R') - U(n)/T"from the configuration space of n ordered distinct points of R3 to the flag manifold of U(n)which is compatible with the natural action of the symmetric group Z. on both spaces. Ialso noted in [1] that the action of E. on the rational cohomology of either space coincideswith the regular representation but that the homomorphism f* induced by f cannot possiblybe an isomorphism. In fact the…     

THE GROWTH THEOREM FOR QUASI-CONVEX MAPPINGS IN HILBERT SPACES

In this paper, the authors extend the definition of quasi-convex mappings and obtain the corresponding growth theorem.on the unit ball of a complex Hilbert space X.     

阶化Cartan型李代数的上同调

本文利用广义限制李代数的概念和应用Frobenius代数的一些性质来研究广义限制李代数的广义限制完备上同调,并利用广义限制上同调与通常上同调的关系尝试着给出一种计算系数为不可约模的阶化Cartan型李代数上同调的方法.     

Hilbert变换在Banach值Hardy空间上的有界性

本文给出了Ｈｉｌｂｅｒｔ变换在Ｂａｎａｃｈ空间值Ｈａｒｄｙ空间ＨＢ＾１（Ｒ）上的有界性。     

Hilbert空间中非Lipschitz连续半群的几乎轨道的渐近行为

本文研究{u(t))的渐近行为．证明了{u(t))几乎弱收敛到集∩co{u(t)：t≥s}∩F(T)的唯一点．利用该结果，推得。{u(t))弱收敛到T的不动点。当且仅当对每个h≥0，当t→∞时{u(t h)-u(t)}弱收敛到零向量．     

HOMOLOGY AND COHOMOLOGY FOR MEROTOPIC AND NEARNESS SPACES

It is shown that the Alexander cohomology groups for merotopic spaces satisfy certain variants of the Eilenberg—Steenrod axioms for a cohomology theory. Furthermore, for a nearness space, the homology and cohomology groups coincide with the corresponding groups of its completion.     

Elementary counterexamples to Kodaira vanishing in prime characteristic

Using methods from the modular representation theory of algebraic groups one can construct [1] a projective homogeneous space forSL ₄, in prime characteristic, which violates Kodaira vanishing. In this note we show how elementary algebraic geometry can be used to simplify and generalize this example.     

HILBERT空间中散逸动力系统一般线性方法的散逸稳定性

１．引言 １９９４年,Ｓｔｕａｒｔ与 Ｈｕｍｐｈｒｉｅｓ［４,５］首先考察了用 Ｒｕｎｇｅ－Ｋｕｔｔａ方法求解 Ｒｍ中的散逸动力系统（２．１）－（２．２）时数值解是否继承真解具有的散逸稳定性,并表明代数稳定且不可约的 Ｒｕｎｇｅ－Ｋｕｔｔａ方法是散逸稳定的且有一有界吸引集．１９９６年,本文作者［１］把这一工作推广到了两类特殊的一般线性方法．１９９７年,Ｈｉｌｌ在［３］中证明了Ａ－稳定是单支方法散逸稳定的充要条件,在［２］中又把文［４,５］的工作推广到了 Ｈｉｌｂｅｒｔ空间中的散逸动力系统（２．１）－（…     

ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS

0.IntroductionThispaperisaimedatdevelopingthecohomologytheoryofmodularLiealgebrasandthendeterminingthefirstcohomologygroupsofCartantypeLiealgebras.AsgeneralizationoftheconceptofrestrictedLiealgebras,ageneralizedrestrictedLiealgebra(GRLiealgebra)wasintroducedin[21],whichisassociatedwithabasisandamappingofthebasisintotheLiealgebrasatisfyingthegeneralized-restrictednessconditions.Generalizedrestrictedrepresentations(GRrepresentations)werethenintroduced,whichcanbereducedtotherepresentationsofa…     

NORM RETRIEVAL BY PROJECTIONS ON INFINITE-DIMENSIONAL HILBERT SPACES

We study the norm retrieval by projections on an infinite-dimensional Hilbert space H. Let {e_i}_(i∈I)be an orthonormal basis in H and W_i= {e_i}~⊥for all i ∈ I. We show that {W_i}_(i∈I)does norm retrieval if and only if I is an infinite subset of N. We also give some properties of norm retrieval by projections.     

EXISTENCE AND CONTROLLABILITY FOR NONLINEAR FRACTIONAL CONTROL SYSTEMS WITH DAMPING IN HILBERT SPACES

In this paper, we are concerned with the existence of mild solution and controllability for a class of nonlinear fractional control systems with damping in Hilbert spaces.Our first step is to give the representation of mild solution for this control system by utilizing the general method of Laplace transform and the theory of(α, γ)-regularized families of operators. Next, we study the solvability and controllability of nonlinear fractional control systems with damping under some suitable sufficient conditions. Finally, two examples are given to illustrate the theory.     

GENERAL SPLIT FEASIBILITY PROBLEMS FOR TWO FAMILIES OF NONEXPANSIVE MAPPINGS IN HILBERT SPACES

The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.     

复Stiefel流形的商空间

本文研究了复Stiefel流形关于群S1的商空间的伦型,并且计算了该空间的上同调群.通过纤维化,为这些商空间的上同调找到一组典则的生成元.再利用推广的吴公式,讨论了这些生成元在Sqi下的行为.最后,作为应用,本文对S.Gitler和D.Handel的结果作了部分改进.     

HILBERT SPACES OF FUNCTIONALS ASSOCIATED WITH NONLINEAR OPERATORS

Abstract

In [7] the subject of reproducing kernel Hilbert spaces (RKHSs) of linear functionals associated with linear operators and, in particular, with second-order generalized stochastic processes (GSPs), is pursued. In this work these ideas are extended to nonlinear operators. As an example the characteristic operator of a GSP is pursued. The so-called nonlinear space of the process associated with the characteristic operator is investigated and the RKHS of functionals isometrically isomorphic to it is constructed. Unlike the linear space, the nonlinear analysis is not limited to second order GSPs.     

随机微分—积分方程解的存在唯一性

本文讨论Ｈｉｌｅｒｔ空间中非线性随机微分－积分方程解的存在性,唯一性,在我们所 一组条件下,得到了解的局部存在唯一性的结果。     

THE GENERALIZED ROPER-SUFFRIDGE OPERATOR ON THE UNIT BALL IN COMPLEX BANACH AND HILBERT SPACES

In this paper,we extend the Roper-Suffridge extension operator in complex Banach space,and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit ball in complex Banach spaces. Thereby,we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spirallike mappings in several complex variables.     

具有高消失矩的3-进双正交对称小波的构造

本文用矩阵对称扩充来构造了具有高消失矩的3带对称双正交小波.利用矩阵扩充,获得了3维矩阵对称扩充方法和小波构造的算法,并且,该算法便于计算机程序化实现;利用两个实例验证了相关的结论.     

BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS

In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter α goes to zero.