可拓概率空间讨论

本文提出了Ⅰ型和Ⅱ型可拓概率空间两个概念,并讨论了它们的一般性质     

On an abstract integro-differential problem

In an arbitrary Banach space we consider the Cauchy problem for an integro-differential equation with unbounded operator coefficients. We establish the solvability of the problem in the weight spaces of integrable functions under certain conditions on the data. To prove this, the solution of the problem is written in explicit form with the help of analytic semigroups generated by fractional powers of the operator coefficients. Here an important role is played by the conditions on the coefficients ensuring the coercive estimates of the corresponding integral operators. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 887–896, December, 1999.     

等距线性延拓问题

本文引入了两个赋范空间的单位球面间等距映射的延拓问题,并且列出了相关问题的一些重要结果和近期的进展.     

The representation theorem of onto isometric mappings between two unit spheres of l∞-type spaces and the application on isometric extension problem

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of real l∞-type spaces, then we conclude that such mappings can be extended to the whole space as (real) linear isometries.     

Integral representation of random set-valued measures

Abstract

We consider random set-valued measures with values in a separable Banach space. We prove two integral representation theorems using measurable multifunctions and set-valued integrals. The first theorem is valid for all separable Banach spaces, while the second holds for reflexive separable Banach spaces.     

Linear Bilipschitz Extension Property

We give a sufficient geometric condition for a subset A of R ⁿ to enjoy the following property for a fixed C1: There is >0 such that for 0, each (1+)-bilipschitz map f: AR ⁿ extends to a (1+C)-bilipschitz map F: R ⁿ R ⁿ .     

On isometric extension problem between two unit spheres

In this paper we introduce the isometric extension problem of isometric mappings between two unit spheres. Some important results of the related problems are outlined and the recent progress is mentioned.     

Cauchy-type problem for an abstract differential equation with fractional derivatives

The uniform well-posedness of a Cauchy-type problem with two fractional derivatives and bounded operator A is proved. For an unbounded operator A we present a test for the uniform well-posedness of the problem under consideration consistent with the test for the uniform well-posedness of the Cauchy problem for an equation of second order.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 28–41.Original Russian Text Copyright © 2005 by A. V. Glushak.This revised version was published online in April 2005 with a corrected issue number.     

一致连续映射的两个扩张定理

把文[1],[2]中的两个定理进行了拓广和改进,给出两个一致连续映射的扩张定理:(i)任一集合A到一个完备度量空间的一致连续映射可一致连续扩张到A珡上.(ii)任一闭集A到Rn的一致连续映射可一致连续扩张到A与任一紧集的并.     

可测空间的算子扩张及其上的等价关系

讨论可测空间（U，σU))的两种不同的扩张，使其满足任意并（交）的封闭性，并证明二者是等价的，找到了利用可测空间（U，σ（U））的算子的扩张空间（U，σ^*（U))中的上（下）方逼近算子定义的一个等价关系。     

On a generalized Mazur-Ulam question: Extension of isometries between unit spheres of Banach spaces

We call a Banach space X admitting the Mazur-Ulam property (MUP) provided that for any Banach space Y, if f is an onto isometry between the two unit spheres of X and Y, then it is the restriction of a linear isometry between the two spaces. A generalized Mazur-Ulam question is whether every Banach space admits the MUP. In this paper, we show first that the question has an affirmative answer for a general class of Banach spaces, namely, somewhere-flat spaces. As their immediate consequences, we obtain on the one hand that the question has an approximately positive answer: Given ε>0, every Banach space X admits a (1+ε)-equivalent norm such that X has the MUP; on the other hand, polyhedral spaces, CL-spaces admitting a smooth point (in particular, separable CL-spaces) have the MUP.     

集值映射的可测性与连续性

引进《集D关于集β对于关系《是正常的》这个概念,由两个单值映射组成,再通过取凸包和闭包,构造了可测集值映射、上下半连续集值映射和连续集值映射.     

Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term

In a Banach space E, we consider the inverse problem du(t)/dt = Au(t) + (t)p , u(0) = u ₀, u(T) = u₁, with an unknown function u(t) and an element p E. The operator A is assumed linear and closed. In this paper, we establish minimal constraints on the function C([0, T]) for which the uniqueness of the solution of the inverse problem is completely described in terms of the eigenvalues of the operator A.Translated from Matematicheskie Zametki, vol. 77, no. 2, 2005, pp. 273–290.Original Russian Text Copyright © 2005 by I. V. Tikhonov, Yu. S. Éidelman.This revised version was published online in April 2005 with a corrected issue number.     

一个不等式的拓广

Kantorovich 不等式的推广文〔4〕给出了x′Ay y′A~(-1)x/(x′xyy′)的上界,其中A是n 阶实正定阵,x、y 是n 维非零实向量。本文给出x′Ay y′A~(-1)x/(x′xy′y)的上界和下界,其中A 是任何n×m 实矩阵,A~(-1)是A 的广义加号逆,x、y 分别是n 维和m 维非零实向量。     

The generalized optimality conditions of multiobjective programming problem in topological vector space

In this study, an alternative theorem for the subconvexlike mapping in topological vector space is established. With this alternative theorem as an aid, the generalized Fritz John conditions and the generalized Kuhn-Tucker conditions in terms of Gâteaux derivatives of multiobjective programming problem in the ordered topological vector space are given.     

An inverse problem with final time additional condition for an abstract evolution equation in an ordered Banach space

Moscow Institute for Physical Engineering. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 27, No. 1, pp. 81–83, January–March, 1993.     

关于α次的殆星映射推广的Roper-Suffridge算子的一个注记

Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Φn, β2, γ2, …, βn, γn (f)(z) = (f(z1), (f(z1)/z1)β2(f'(z1))γ2z2,…,(f(z1)/z1)βn(f'(z11))γnzn)' preserves almost starlikeness of order α on Ωn,p1,p2,…,pn = {z =(z1,z2,…,zn)' ∈ Cn n∑j=1 |zj|pj ＜ 1}, where 0 ＜ p11 ≤ 2, pj ≥ 1, j = 2,…,n, are real numbers.     

关于Hilbert空间单位球面上等距延拓的注记

本文指出,文[1]中有关在单位球面S1[H]上的1-Lipschitz假设条件减弱为“局部1-Lipschitz”条件时,那里的等距定理仍然成立.     

Analytic Extension of Functions from Analytic Hilbert Spaces

Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd).     

On the solvability of an abstract Cauchy problem

We consider the Cauchy problem for a first-order linear inhomogeneous differential equation for functions ranging in a Banach space in the case of a sectorial operator coefficient. We find conditions for the solvability of the Cauchy problem for the case in which the right-hand side is not necessarily a Hölder function.