非E_2类二阶椭圆组的强非线性R－H边值问题

本文研究非Ｅ_２类二阶椭圆组强非线性Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ边值问题，应用Ｔｉｋｈｏｎｏｖ方法和摄动理论及对近似解序列的先验估计，讨论了边值问题在Ｈａｒｄｙ函数类中的可解性．     

一般形式的一阶椭圆型偏微分方程组拟线性Riemann-Hilbert问题

在文[1,2,3]中,E.Wegert和L.V.Wolfersdorf等人讨论了一类全纯函数的拟线性Riemann-Hilbert问题在Hardy空间中的可解性,在文[4]中,讨论了广义解析函数的拟线性Riemann-Hilbert问题,同样得到该边值问题在H2类解空间中的可解性.本文在前面研究工作的基础上,对一般形式的一阶椭圆型偏微分方程组拟线性Riemannn-Hilbert问题作了更深入的讨论,在适当的假设条件下,应用积分算子理论,函数论方法及不动点原理,证明了该边值问题在相应的泛函空间中同样是可解的.     

一阶椭圆型复方程组Riemann－Hilbert边值问题

本文以解析函数的边值问题Ｂ的解的存在性为基础，根据它们的先验估计式及利用参数开拓法，导出了满足条件Ｃ的多个复变量的一阶拟线性椭圆型复方程组的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ边值问题的可解条件，并给出了解的积分表达式．     

多复变解析函数在多圆环柱域上的Riemann—Hilbert边值问题

本文研究多个复变数解析函数在多圆环柱域上的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ边值问题。对比问题给出了相应变态问题的提法，从而得到问题的可解条件和解的积分表示式。     

一般区域上在边界退化的拟线性抛物方程的第—初边值问题

对有界域上拟线性抛物方程第一初边值问题，二阶退化拟线性抛物方程初边值问题已有丰富的成果，可见［１］，［２］，［３］，但对任意域上方程的工作则不多见．在此文中，我们讨论任意区域上在边界退化的拟线性抛物方程初边值问题的存在性．     

多圆柱域上带间断系数的边值问题

本文研究多个复变数解析函数在多圆柱区域上带间断系数的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ边值问题。文中给出了这个问题适定的变态提法，首先证明了相应变态问题解的存在唯一性。然后给出原边值问题可解的充要条件及解的积分表达式。     

一阶椭圆型复方程组Riemann—Hibert边值问题

本文以解析函数的边值问题Ｂ的解的存在性为基础，根据它们的先验估计式及利用参数开拓法，导出了满足条件Ｃ的多个复变量的一阶拟线性椭圆型复方程组的Ｒｉｅｍａｎｎ－Ｈｉｂｅｒｔ边值问题的可解条件，并给出了解的积分表达式。     

伪抛物型复方程的Riemann─Hilbert初边值问题的可解性及其近似解的误差估计

本文使用参数开拓法证明了非线性伪抛物型复方程在多连通区域上的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ初边值问题的可解性，并对近似解作出了误差估计。     

伪抛物型复方程的Riemann—Hilbert初边值问题的可解性及其…

本文使用参数开拓法证明了非线性伪抛物型复方程在多连通区域上的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ初边值问题的可解性，并对近似解作出了误差估计。     

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）－（…     

一类Riemann-Hilbert边值逆问题

给出解析函数的一类R iem ann-H ilbert边值逆问题的数学提法,依据解析函数R iem ann-H ilbert边值问题的经典理论,讨论了此边值问题的可解性,给出了该边值问题的可解条件和解的表示式.     

The mixed joint universality for a class of zeta‐functions

A mixed joint limit theorem in the space of holomorphic functions, and a mixed joint universality theorem are proved for a rather general class of Euler products and periodic Hurwitz zeta‐functions.     

Über holomorphe und meromorphe einseitige Inverse

In this note a theorem of B. Gramsch [6] on one-sided meromorphic inverses of Semi-Fredholmoperator valued holomorphic functions is generalized to holomorphic functions on a Stein space with values in the set of Semi-Fredholm-operators between two Banach spaces. By the way, a theorem of G.R. Allan [1] on holomorphic one-sided inverses is generalized to holomorphic functions on a Stein space with values in certain paraalgebras (c.f. [5]). As an application of that a duality theorem for holomorphic bases of finite dimensional subspaces of (F)- and (DF)-spaces is proved (c.f. [3]).     

一类广义解析函数的Riemann边值逆问题

本文给出了一类有关广义解析函数Riemann边值逆问题的数学提法．在将此边值逆问题转化为边值问题的基础上，借助于广义解析函数边值问题的相关理论，分别获得了此边值逆问题在正则型和非正则型情况下的解．     

一类拟线性抛物型方程解的爆破时间的下界

本文巧妙应用广义Sobolev不等式,研究了一类拟线性抛物型方程解的爆破时间的下界,该结果推广了文献[1]中的定理2.1和定理3.1的结论,同样完善了文献[2]中的模型(4.1)的结论.     

A new method for solving singular fourth-order boundary value problems with mixed boundary conditions

In [1], [2], [3], [4], [5], [6], [7] and [8], it is very difficult to get reproducing kernel space of problem (1). This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of fourth-order in the new reproducing kernel space. The numerical results are compared with both the exact solution and its n-order derived functions in the example. It is demonstrated that the new method is quite accurate and efficient for fourth-order problems.     

Multiplicative Decompositions of Holomorphic Fredholm Functions and ψ*-Algebras

In this article we construct multiplicative decompositions of holomorphic Fredholm operator valued functions on Stein manifolds with values in various algebras of differential and pseudo differential operators which are submultiplicative ψ* - algebras, a concept introduced by the first author. For Fredholm functions T(z) satisfying an obvious topological condition we. Prove (0.1) T(z) = A(z)(I + S(z)), where A(z) is holomorphic and invertible and S(z) is holomorphic with values in an “arbitrarily small” operator ideal. This is a stronger condition on S(z) than in the authors' additive decomposition theorem for meromorphic inverses of holomorphic Fredholm functions [12], where the smallness of S(z) depends on the number of complex variables. The Multiplicative Decomposition theorem (0.1) sharpens the authors' Regularization theorem [11]; in case of the Band algebra L(X) of all bounded linear operators on a Band space, (0.1) has been proved by J. Letterer [20] for one complex variable and by M. 0. Zaidenberg, S. G. Krein, P. A. Kuchment and A. A. Pankov [26] for the Banach ideal of compact operators.     

ON THE CONVERGENCE OF PADE-TYPE APPROXIMANTS IN TWO VARIABLES

In [1], C. Brezinski raised three unsolved questions in studing multivariable Pade-iype approximation, and the convergence of multivariable Pade-iype approximants under the general conditions is one of them. We have only seen in [2] that the convergence of the mullivariable Fade-type approximants is discussed for a kind of functions defined by Stieltjes integrations under some special conditions. However, the general convergence theorem has not been seen so far. In this paper, some error formulae of bivariate Fade-type approximants in in-legral form are given. By virtue of them, a number of convergence theorems of bivariate Pade-iype approximants are proved under general conditions.     

ON BOUNDARY VALUE PROBLEMS FOROVERDETERMINED ELLIPTIC SYSTEMS OF TWO COMPLEX VARIABLES

In this paper,based on previous results,the Riemann-Hilbert boundary valueproblems with general forms for overdetermined elliptic equations of first order are consi-dered.The characteristic of modified function space is given.It is proved that there existsa unique solution for modified problem of the problem which we discuss.By the way,itis pointed out that there are great differences between overdetermined elliptic systems andfirst order elliptei systems in the plane.     

Optimal uniform approximation on angles by entire functions

The paper discusses the best or optimal uniform approximation problem by entire functions on a closed angle Δ. This problem has been studied by M.V. Keldysch in [4], under the assumption that the functions ? subject to approximation are holomorphic in a larger angle containing Δ and there is no restriction on the growth of ? at infinity. In [8], the problem was investigated for a wider class of functions ? continuously complex differentiable on Δ, with sharper estimates on the growth of approximating entire functions, linked with the growth of ? on Δ and the differential properties of ? on the boundary of Δ. In this paper, we improve some of the results on entire approximation on angles, using new approximation ideas partially presented in [9] and [10].