COHOMOLOGY VANISHING IN HILBERT SPACES

§1. Introduction Oka [40] proved that any additive Cousin problem is solvable in a domain of holomorphyin Cn. Oka [41]-Cartan [2, 3]-Serre [46] generalized this as the theorem B for analyticcoherent sheaves over Stein spaces. J. P. Serre [47] proved…     

THE δ^－－PROBLEM FOR HOLOMORPHIC （0,2）－FORMS ON PSEUDOCONVEX DOMAINS IN SEPARABLE HILBERT SPACES AND D.F.N. SPACES

This paper shows that the δ^--problem for holomorphic (0, 2)-forms on Hilbert spaces is solv-able on pseudoconvex open subsets. By using this result, the authors investigate the existence ofthe solution of the δ^--equation for holomorphic(0, 2)-forms on pseudoconvex domains in D.F.N.spaces.     

A NOTE ON REARRANGEMENTS OF SERIES IN BANACH SPACES

We generalize Kadec‘s and Yan Zikun‘s resuhs in [1],[2] to prove; in every infinite dimensional real Banach space Y there exist an infinite dimensional subspace X and a series ∑xn such that ∑xn has property(N) in X. but(the domain of sums of this series) S(∑xn) is not a convex set.     

集值映射的变分不等式和补问题及应用

The purpose of this paper is to study the variational inequality and complementarity problem for set-valued mapping in Banach spaces.The results presented in this paper generalize and improve some recent results on finite dimensional spaces,Hiblert spaces,single-valued mapping.As applications.we utilize our results to study saddle point problems and two programming problems in infinite dimensional spaces.     

INTERPOLATION OF Ba SPACES

In this paper we advance the interpolation theorems of linear operator in Ba spaces. The conception of Ba spaces was first put forward by Ding Xiaxi in his discussion on the prior estimate of Laplace operator in some classical domains and in his study of the embedding theorem of Orlicz-Sobolev spaces, higher dimensional singular     

QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES

Let f : U(x0) (?) E→F be a. C1 map and f'(X0) be the Prechet derivative of /fat X0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties: f'(x0) is double splitting and R(f'(x))∩N(T0 ) = {0} near X0. However, in infinite dimensional Banach spaces, f'(x0) is not always double splitting (i.e., the generalized inverse of f'(xo) does not always exist), but its bounded outer inverse of f'(x0) always exists. Only using the C1 map f and the outer inverse T0# of f'(x0), the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if X0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.     

ON SPACES OF FRACTAL FUNCTIONS

In this paper we Ointroduce linear-spaces consisting of continuous functions whose graphs are the attactars of a special class of iterated function systems. We show that such spaces are finite dimensional and give the bases of these spaces in an implicit way. Given such a space, we discuss how to obtain a set of knots for whah the Lagrange interpolation problem by the space is uniquely solvable.     

Axisymmetric stokes exterior problem and its numerical computation

We establish variational formulation and prove the existence and uniqueness of the three dimensional axisymmetric Stokes exterior problem in weighted spaces.Error estimates and convergence for P2-P0 elements with infinite element methods are also obtained.Numerical experiments are presented to verify the theoretical analysis.     

Nonstandard Analysis Methods for Separations in[0,1]-topological Spaces

In nonstandard enlargement,the separations are characterized by nonstandard analysis methods in[0,l]-topological spaces.Firstly,the monads of fuzzy point in[0,l]-topological spaces are described with remote-neighborhoods in nonstandard enlarged model.Then the nonstandard characterizations of separations in [0,l]-topological space are given by the monads.At last,relations of these separations are investigated.     

THE PROPAGATION OF NONSTATIONARY FILTRATION WITH ABSORPTION

We point out a mistake in [1] in the proof of infinite propagation of the weak solution of Cauchyproblem for the equation u_(?)=(A(u))_(xx)=(?)(u).A more natural condition is given and the infinitepropagation property for boundary value problem is studied.Finally,we discuss the supports of theweak solutions.     

Controllability of Linear Systems in Non Reflexive Banch Spaces

§ 1.Introduction　 Let Xand Ube Banch spaces,S(t) a C0 semi-group in X,A the infinitesimal gen-erator of S(t) ,and B∈L(U,X) .Consider the systemΣP:x(t) =Ax(t) + Bu(t) ,　 t≥ 0 ,(1 .1 )where u∈ Lploc([0 ,∞ ) ,U) ,1≤p<∞ .　 The problem of controllability of linear systems in Banch spaces has been studied bymany authors.In [1 ] ,the weak and strong reachability and controllability of infinite di-mensional linear systems were investigated.In[2 ,3 ,4 ] ,the controllability of infi…     

THE SPACES OF CESARO ALMOST CONVERGENT SEQUENCES AND CORE THEOREMB

As known,the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces.However,the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new(see [15]).The purpose of this paper is to introduce the new spaces f and f0 consisting of all sequences whose Cesa`ro transforms of order one are in the spaces f and f0,respectively.Also,in this paper,we show that f and f0 are linearly isomorphic to the spaces f and f0,respectively.The β-and γ-duals of the spaces f and f0 are computed.Furthermore,the classes(f:) and(:f) of infinite matrices are characterized for any given sequence space,and determined the necessary and sufficient conditions on a matrix A to satisfy BC-core(Ax) K-core(x),K-core(Ax) BC-core(x),BC-core(Ax) BC-core(x),BC-core(Ax) st-core(x) for all x ∈∞.     

ISOMETRIC APPROXIMATIONS FROM UNIFORMLY SMOOTH SPACES INTO l_∞(Ⅰ') TYPE SPACES

In this paper we've proved that if X is a uniformly smooth Banach space, then the IAP (isometric approximation problem)on the space B(X, l_∞(Γ)) for some infinite index set Γ is aftirmative if and only if dimX=l or ∞. Particularly the IAP on spaces B(l_p, m) and B(L_p[0, 1], m) are affirmative(1相似文献   

APPROXIMATING SOLUTION OF 0∈ T（x） FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES

The purpose of this paper is to study the solution of 0 ∈ T (x) for an H-monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145(2003)795-803] in Hilbert spaces, which is the first pro...     

KAM tori for higher dimensional beam equation with a fixed constant potential

In this paper, we consider the higher dimensional nonlinear beam equation:utt + △2u + σu + f(u)=0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u)=u3+ h.o.t near u=0 and σ is a positive constant. It is proved that for any fixed σ>0, the above equation admits a family of small-amplitude, linearly stable quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.     

Some specific unboundedness property in smoothness Morrey spaces. The non-existence of growth envelopes in the subcritical case

We study smoothness spaces of Morrey type on Rn and characterise in detail those situations when such spaces of type A_(p,q)~(s,r)(R~n) or A_(u,p,q)~s(R~n) are not embedded into L_(∞)(R~n).We can show that in the so-called sub-critical,proper Morrey case their growth envelope function is always infinite which is a much stronger assertion.The same applies for the Morrey spaces M_(u,p)(R~m) with p u.This is the first result in this direction and essentially contributes to a better understanding of the structure of the above spaces.     

On the Same $n$-Types for the Wedges of the Eilenberg-Maclane Spaces

Given a connected CW-space X, SN T(X) denotes the set of all homotopy types[X′] such that the Postnikov approximations X~((n)) and X′~((n)) are homotopy equivalent for all n. The main purpose of this paper is to show that the set of all the same homotopy ntypes of the suspension of the wedges of the Eilenberg-MacL ane spaces is the one element set consisting of a single homotopy type of itself, i.e., SNT(Σ(K(Z, 2a_1) ∨ K(Z, 2a_2) ∨···∨ K(Z, 2a_k))) = * for a_1 a_2 ··· a_k, as a far more general conjecture than the original one of the same n-type posed by McG ibbon and M?ller(in [McG ibbon, C. A. and M?ller, J. M., On infinite dimensional spaces that are rationally equivalent to a bouquet of spheres, Proceedings of the 1990 Barcelona Conference on Algebraic Topology, Lecture Notes in Math., 1509, 1992, 285–293].)     

QUALITATIVE THEORIES OF CONSTRUCTIONS OF Q-PROCESSES ON ABSTRACT SPACES

Introduction The qualitative theories of the constructions of q-processes on countable spaces were established by Hou Zhenting and Guo Qingfeng ([7] or [1,Chapter 14]).In[4]the definition of q-processes on abstract spaces were mentioned, and the criterion for existence and for     

CALDER6N-ZYGMUND OPERAORS ON THE HARDY SPACES OF WEIGHTED HERZ TYPE

Applying the decomposition theorems in [1] and [2] , we obtain the boundedness theorem of Calderbn-Zygmund operator of type 6 on the Hardy spaces of weighted Herz type and establish interpolation theorem of linear operators on the weighted Herz spaces. -     

Ba SPACES AND NAVIER-STOKES EQUATIONS

§1. Introduction In this paper we consider the continuous dependence of the solutions of the Cauchy problem for Navier-Stokes equations on theirs initial data in various function spaces, the Nikol'ski space H_2~(1+l) and Ba space. The Ba space was introduced by Ding Xiaxi and Into Peizhu, as follows