复超球Bergman空间和Bloch空间上的Carleson不等式

本文研究了复超球上Ｃａｒｌｅｓｏｎ测度的特征．特别是用Ｂｅｒｇｍａｎ函数和Ｂｌｏｃｈ函数的导数的积分性质刻画了Ｃａｒｌｅｓｏｎ测度，并建立了复超球上的Ｂｅｒｇｍａｎ空间和Ｂｌｏｃｈ空间的Ｃａｒｌｅｓｏｎ不等式．     

非线性算子方程迭代解的存在性定理及其应用

在Ｂａｎａｃｈ空间中,利用锥理论和单调迭代方法研究了一类非线性算子方程的解和最小最大耦合解的存在与迭代逼近定理,并应用到Ｂａｎａｃｈ空间中非线性Ｖｏｌｔｅｒｒａ型积分方程和常微分方程的初值问题．     

实Clifford分析中六类拟Bochner-Martinelli型高阶奇异积分的几个问题

本文借助于Ｈａｄａｍａｒｄ关于高阶奇异积分有限部分的思想,研究关于实 Ｃｌｉｆｆｏｒｄ分析中六个类型(含一个奇点或二个奇点的)拟Ｂｏｃｈｎｅｒ－Ｍａｒｔｉｎｅｌｌｉ型高阶奇异积分的归纳定义、Ｈａｄａｍａｒｄ主值的存在性、递推公式、计算公式、微分公式、Ｐｏｉｎｃａｒｅ－Ｂｅｒｔｒａｎｄ置换公式以及拟Ｂ－Ｍ型高阶奇异积分的Ｈｏｌｄｅｒ连续性等问题．这些问题是研究单、多元复分析的学者们在研究奇异积分时,通常要涉及到的几个问题．     

Banach空间非线性混合单调Hammerstein型积分方程的迭代解

在Ｂａｎａｃｈ空间中，建立了“非线性混合单调型算子”不动点和最大最小耦合不动点的存在与迭代逼近定理，并应用到序Ｂａｎａｃｈ空间非线性混合单调Ｈａｍｍｅｒｓｔｅｉｎ型积分方程．     

序Banach空间中算子方程的迭代求解及其应用

利用半序理论和混合单调算子技巧,研究序Ｂａｎａｃｈ空间中非线性算子方程解的存在唯一性,并给出了迭代序列收敛于解的误差估计．作为应用,讨论了序Ｂａｎａｃｈ空间中一类非线性积分方程的可解性,改进和推广了某些已知结果．     

Banach空间上的框架与拟Riesz基

该文首先给出Ｂａｎａｃｈ空间上的框架与拟Ｒｉｅｓｚ基的充要条件,其次讨论Ｂａｎａｃｈ空间上的框架和拟Ｒｉｅｓｚ基的稳定性,特别地,讨论在Ｂａｎａｃｈ空间上关于框架与拟Ｒｉｅｓｚ基的广义Ｐａｌｅｙ Ｗｉｅｎｅｒ定理．     

Banach空间中超线性Hammerstein型积分方程的解及其应用

本文利用不动点指数理论研究Ｂａｎａｃｈ空间中超线性Ｈａｍｍｅｒｓｔｅｉｎ型积分方程正解及非零解的存在性，并应用于Ｂａｎａｃｈ空间中超线性常微分方程的Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｌｅ问题，最后，本文给出了一个非线性常微分方程无穷组存在正解的例子．     

向量值Laplace变换与右连续积分半群

该文利用向量值Ｌａｐｌａｃｅ变换给出一类向量值函数的表示，并将它应用于Ｂａｎａｃｈ空间的Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质的刻划，引进了右连续积分半群，证明了一类非稠定且指数增长的算子对应的Ｃａｕｃｈｙ问题是适定的．     

Plemelj公式及其应用

本文介绍了Ｃ￣ｎ空间中函数经Ｂｏｃｈｎｅｒ－Ｍａｒｔｉｎｅｌｌｉ变换后的Ｐｌｅｍｅｌｊ公式和它在Ｓｔｅｉｎ流形上的拓广，同时还介绍了Ｃ￣ｎ空间和Ｓｔｅｉｎ流形上微分形式在Ｂｏｃｈｎｅｒ－Ｍａｒｔｉｎｅｌｌｉ变换下的跳跃公式以及这些公式分别在全纯开拓，闭开拓，方程和线性奇异积分方程上的应用．     

非拟牛顿非凸族的收敛性

１．引言 对于无约束最优化问题拟牛顿法是目前最成熟,应用最广泛的解法之一．近二十多年来,对拟牛顿法收敛性质的研究一直是非线性最优化算法理论研究的热点．带非精确搜索的拟牛顿算法的研究是从１９７６年 Ｐｏｗｅｌｌ［１］开始,他证明了带 Ｗｏｌｆｅ搜索 ＢＦＧＳ算法的全局收敛性和超线性收敛性． １９７８年 Ｂｙｒｄ, Ｎｏｃｅｄａｌ; Ｙａ－Ｘｉａｎｇ Ｙｕａｎ［３］成功地将 Ｐｏｗｅｌｌ的结果推广到限制的 Ｂｒｏｓｄｅｎ凸族． １９８９年, Ｎｏｃｅｄａｌ［４］在目标函数一致凸的条件下,证明了带回追搜索的ＢＦＧ…     

On Vector Integral Inequalities

The first author introduced an integration theory of vector functions with respect to an operator-valued measure in complete bornological locally convex vector spaces. In this paper some important results behind this Dobrakov-type integration technique in non-metrizable spaces are given. Received: December 10, 2007., Accepted: May 6, 2008.     

On Integrable Functions in Complete Bornological Locally Convex Spaces

A Lebesgue-type integration theory in complete bornological locally convex topological vector spaces was introduced by the first author in [17]. In this paper we continue developing this integration technique and formulate and prove some theorems on integrable functions as well as some convergence theorems. An example of Dobrakov integral in non-metrizable complete bornological locally convex spaces is given.     

An application of bilinear integration to quantum scattering

Scattering theory has its origin in Quantum Mechanics. From the mathematical point of view it can be considered as a part of perturbation theory of self-adjoint operators on the absolutely continuous spectrum. In this work we deal with the passage from the time-dependent formalism to the stationary state scattering theory. This problem involves applying Fubini's Theorem to a spectral measure integral and a Lebesgue integral of functions that take values in spaces of operators. In our approach, we use bilinear integration in a tensor product of spaces of operators with suitable topologies and generalize the results previously stated in the literature.     

Discrete pseudo-integrals

Integration of simple functions is a corner stone of general integration theory and it covers integration over finite spaces discussed in this paper. Different kinds of decomposition and subdecomposition of simple functions into basic functions sums, as well as different kinds of pseudo-operations exploited for integration and sumation result into several types of integrals, including among others, Lebesgue, Choquet, Sugeno, pseudo-additive, Shilkret, PAN, Benvenuti and concave integrals. Some basic properties of introduced discrete pseudo-concave integrals are discussed, and several examples of new integrals are given.     

Set-valued functions,Lebesgue extensions and saturated probability spaces

Recent advances in the theory of distributions of set-valued functions have been shaped by counterexamples which hinge on the non-existence of measurable selections with requisite properties. These examples, all based on the Lebesgue interval, and initially circumvented by Sun in the context of Loeb spaces, have now led Keisler and Sun (KS) to establish a comprehensive theory of the distributions of set-valued functions on saturated probability spaces (introduced by Hoover and Keisler). In contrast, we show that a countably-generated extension of the Lebesgue interval suffices for an explicit resolution of these examples; and furthermore, that it does not contradict the KS necessity results. We draw the fuller implications of our theorems for integration of set-valued functions, for Lyapunov's result on the range of vector measures and for the theory of large non-anonymous games.     

On the Riesz representation theorem and integral operators

We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions.     

On the geometry in projective limits of Hilbert spaces

In this paper we consider the concept of orthogonality with respect to infinitely many inner products. We describe geometric properties related to this concept of orthogonality in certain Köthe sequence spaces (power series spaces), spaces of holomorphic functions in one and several variables and spaces of infinitely differentiable functions. The methods are required from a mixture of functional analysis (theory of bases), theory of functions of one complex variable, Fourier analysis and interpolation theory.     

Tractability results for the weighted star-discrepancy

The weighted star-discrepancy has been introduced by Sloan and Wo?niakowski to reflect the fact that in multidimensional integration problems some coordinates of a function may be more important than others. It provides upper bounds for the error of multidimensional numerical integration algorithms for functions belonging to weighted function spaces of Sobolev type. In the present paper, we prove several tractability results for the weighted star-discrepancy. In particular, we obtain rather sharp sufficient conditions under which the weighted star-discrepancy is strongly tractable. The proofs are probabilistic, and use empirical process theory.     

Spaces of integrable functions with respect to a vector measure and factorizations through and Hilbert spaces

We use the integration structure of the spaces of scalar integrable functions with respect to a vector measure to provide factorization theorems for operators between Banach function spaces through Hilbert spaces. A broad class of Banach function spaces can be represented as spaces of scalar integrable functions with respect to a vector measure, but this representation (the vector measure) is not unique. Since our factorization depends on the vector measure that is used for the representation we also give a characterization of those vector measures whose corresponding spaces of integrable functions coincide.     

TRACTABILITY OF MULTIVARIATE INTEGRATION PROBLEM FOR PERIODIC CONTINUOUS FUNCTIONS

The authors study the tractability and strong tractability of a multivariate integration problem in the worst case setting for weighted l-periodic continuous functions spaces of d coordinates with absolutely convergent Fourier series.The authors reduce the initial error by a factor ε for functions from the unit ball of the weighted periodic contin- uous functions spaces.Tractability is the minimal number of function samples required to solve the problem in polynomial in ε~(-1)and d.and the strong tractability is the pres- ence of only a polynomial dependence in ε.This problem has been recently studied for quasi-Monte Carlo quadrature rules.quadrature rules with non-negative coefficients. and rules for which all quadrature weights are arbitrary for weighted Korobov spaces of smooth periodic functions of d variables.The authors show that the tractability and strong tractability of a multivariate integration problem in worst case setting hold for the weighted periodic continuous functions spaces with absolutely convergent Fourier series under the same assumptions as in Ref.[14]on the weights of the Korobov space for quasi-Monte Carlo rules and rules for which all quadrature weights are non-negative.The arguments are not constructive.