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本文给出了关于L0- 线性函数的Hahn-Banach 扩张定理的几何形式并证明这个几何形式等价于它的代数形式. 进一步, 我们利用这个几何形式给出了随机局部凸模中熟知的基本分离定理的一个新的且简单的证明. 最后, 利用这个分离定理, 我们同时在两种拓扑 —(ε, λ)- 拓扑和局部L0- 凸拓扑下证明了随机赋范模中的Goldstine-Weston 稠密性定理, 并举出一个反例说明在局部L0- 凸拓扑下如果随机赋范模不具有可数连接性质, 则Goldstine-Weston 稠密性定理不一定成立. 相似文献
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杨纬隆 《数学物理学报(A辑)》2000,20(2):152-157
关于A3中曲面的H-定理和K-定理是众所周知的了. 该文在此基础上对Weingarten曲面作进一步的研究,得到一个更为广泛的定理. 相似文献
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本文证明一个关于球面S2 到CPN中的共形极小浸入的曲率pinching定理. 相似文献
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文献[1],[2],[3]中讨论了Rn上的局部Hardy空间,并利用乘子定理证明了hp(Rn)=Fp.20(Rn).本文利用Chebyshev等式及正则函数的性质证明了在局部域上有类似的结果hp(Rn)=Fp.20(Rn),从而建立起函数空间之间的关系,并由此给出一个乘子定理. 相似文献
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C∞函数芽的局部奇点理论中,Whitney引理是一个很重要的定理.本文将证明该定理的整体结论.基于这一推广,详细地讨论了一类材料的塑性屈服准则.发现,对于这类材料,塑性屈服准则最一般的形式应是:g(J1,J′2,J′32)=0.最后举例加以说明 相似文献
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本文在广义连续统假设2Nα=Nα+1(简记为GCH)下,给出Banach空间的一个拓扑同构定理。 相似文献
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Summary. We define the multivariate Padé-Bergman approximants (also called Padé approximants) and prove a natural generalization of de Montessus de Ballore theorem.
Numerous definitions of multivariate Padé approximants have already been introduced. Unfortunately, they all failed to generalize
de Montessus de Ballore theorem: either spurious singularities appeared (like the homogeneous Padé [3,4], or no general convergence
can be obtained due to the lack of consistency (like the equation lattice Padé type [3]).
Recently a new definition based on a least squares approach shows its ability to obtain the desired convergence [6]. We improve
this initial work in two directions. First, we propose to use Bergman spaces on polydiscs as a natural framework for stating
the least squares problem. This simplifies some proofs and leads us to the multivariate Padé approximants. Second, we pay a great attention to the zero-set of multivariate polynomials in order to find weaker (although
natural) hypothesis on the class of functions within the scope of our convergence theorem. For that, we use classical tools
from both algebraic geometry (Nullstellensatz) and complex analysis (analytic sets, germs).
Received December 4, 2001 / Revised version received January 2, 2002 / Published online April 17, 2002 相似文献
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George A. Baker 《Studies in Applied Mathematics》1976,55(2):107-117
We prove a theorem which gives necessary and sufficient conditions on the distribution of poles and zeros of the Padé approximants for point-by-point convergence. The special case of convergence to a function meromorphic in a disk by a sequence of Padé approximants free of extraneous poles and zeros is proven. 相似文献
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Convergence conclusions of Padé approximants in the univariate case can be found in various papers. However, results in the
multivariate case are few. A. Cuyt seems to be the only one who discusses convergence for multivariate Pade approximants,
she gives in [2] a de Montessus de Bollore type theorem. In this paper, we will discuss the zero set of a real multivariate
polynomial, and present a convergence theorem in measure of multivariate Padé approximant. The proof technique used in this
paper is quite different from that used in the univariate case.
Supported by National Science Foundation of China for Youth 相似文献
14.
Summary.
For univariate functions the Kronecker theorem, stating the equivalence
between the existence of an infinite block in the table of Padé approximants
and the approximated function being rational, is well-known.
In [Lubi88] Lubinsky proved that if is not rational, then its Padé table
is normal almost everywhere: for an at most countable set of points the
Taylor series expansion of is such that it generates a non-normal
Padé table. This implies that the Padé operator is an almost always
continuous operator because it is continuous when computing a normal
Padé approximant [Wuyt81].
In this paper we generalize the above results to the case of multivariate
Padé approximation. We distinguish between two different approaches for
the definition of multivariate Padé approximants: the general order one
introduced in [Levi76, CuVe84] and the so-called homogeneous one discussed
in [Cuyt84].
Received December 19, 1994 相似文献
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We consider row sequences of (type II) Hermite–Padé approximations with common denominator associated with a vector f of formal power expansions about the origin. In terms of the asymptotic behavior of the sequence of common denominators, we describe some analytic properties of f and restate some conjectures corresponding to questions once posed by A. A. Gonchar for row sequences of Padé approximants. 相似文献
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L. A. Knizhnerman 《Mathematical Notes》2009,86(1-2):81-92
Study of Padé-Faber approximation (generalization of Padéapproximation and Padé-Chebyshev approximation) of Markov functions is important not only from the point of view of mathematical analysis, but also of computational mathematics. The theorem on the existence of subdiagonal approximants is constructively proved. Various estimates of the approximation error are given. Theoretical assertions are illustrated by simulation results. 相似文献
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Milena P. Stojanova 《Constructive Approximation》1988,4(1):435-445
Generalizing the Walsh theorem, E. B. Saff, A. Sharma, and R. S. Varga showed that there is a close relation between the rational interpolants in roots of unity and Padé approximants of certain meromorphic functions. The purpose of this paper is to extend this result, replacing the Padé approximant with other rational functions so as to obtain a larger region of equiconvergence. 相似文献
18.
In this paper we study Padé-type and Padé approximants for rectangular matrix formal power series, as well as the formal orthogonal
polynomials which are a consequence of the definition of these matrix Padé approximants. Recurrence relations are given along
a diagonal or two adjacent diagonals of the table of orthogonal polynomials and their adjacent ones. A matrix qd-algorithm is deduced from these relations. Recurrence relations are also proved for the associated polynomials. Finally a
short presentation of right matrix Padé approximants gives a link between the degrees of orthogonal polynomials in right and
left matrix Padé approximants in order to show that the latter are identical.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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George A Baker 《Journal of Mathematical Analysis and Applications》1973,43(2):498-528
We prove the existence of an infinite number of Padé approximants, and thereby remedy a defect in Nuttall's theorem. It is proved that the sequences of Padé approximants shown by Perron, Gammel, and Wallin to be everywhere divergent contain subsequences which are everywhere convergent. It is further proved that there always exist, for entire functions, everywhere convergent [1, N] and [2, N] subsequences of Padé approximants. There must exist subsequences of [m, N] Padé approximants (N → ∞) which converge almost everywhere in to functions f(z) which are regular except for a finite number (n ? m) of poles in . We prove convergence of the [N, N + j] Padé approximants in the mean on the Riemann sphere for meromorphic functions. 相似文献
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For rectangular matrix functions with restricted sizes of their column and row, we introduce the problem of Padé approximation
similar to its scalar counterpart. Results on the existence and uniqueness of the approximants are given. Determinantal expressions
and some properties of the approximants are established.
Supported by Science Fund for Youth of Chinese Academy of Sciences. 相似文献