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OPTIMAL ALGORITHMS FOR DIAGONAL OPERATORS ON N-WIDTHS IN DIFFERENT COMPUTATIONAL SETTING——In Memory of Professor Sun Yongsheng

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Analysis in Theory and Applications 2007年第2期23卷 180-187页

作者： gensun fang Lixin Qian Beijing Normal University China Beijing Normal University Zhejiang Normal University China

In this paper, we give some optimal algorithms for diagonal operator T from space lp（1≤p≤2） to l2 on n-widths in different computational setting.

关键词： Kolmogorov n-width linear n-width linear average n-width linear stochastic n-width

Recovery of functions via their irregular sampling values

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Chinese Science Bulletin 1998年第4期43卷 268-271页

作者： fang gensun Department of Mathematics, Beijing Normal University, Beijing 100875, China Department of Mathematics Lkijing Normal University Beijing China

It is proved that if a function can be completely reconstructed by tempered splines which satisfy the real Kiesz basis condition as the degree of spline goes to infinity, then the function is band limited.

关键词： band limited function cardinal splines irregular sampling.

Multivariate irregular sampling theorem

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Science China Mathematics 2009年第8期52卷 2469-2478页

作者： CHEN GuangGui fang gensun School of Mathematics and Computer Engineering Xihua UniversityChengdu 610039China School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875China

In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregu... 详细信息

关键词： Marcinkiewicz-Zygmund type inequality multivariate irregular sampling theorem entire function of exponential type 94A20 94A12 41A35 41A80

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ONE-SIDED N-WIDTHS OF SOME CLASSES OF PERIODIC FUNCTIONS

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Analysis in Theory and Applications 1993年第4期9卷 21-36页

作者： fang gensun Zhang Jianhua Beijing Normal University,China Department of Mathematics Beijing Normal University Beijing PRC

In this paper,we determine the exact estimation of one-sided n-widths d_n^+(w_q^r(p_r),L_1).q=1,∝, where W_q^r(P_r)is a class of differentiable 2π-periodic functions,and is determined by a differential opera- tor P_... 详细信息

关键词： Differential Operator Periodic Function Implicit Function Theorem Simple Zero Exact Estimation

Exact n-width on the class of analytic functions in the space of continuous functions

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Progress in Natural Science:Materials International 2005年第8期15卷 761-764页

作者： fang gensun* and LI Xuehua(School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China) Beijing Normal Univ Sch Math Sci Beijing 100875 Peoples R China

Let ω(·) be a given concave modulus of continuity and ω(g,·) be the modulus of continuity of a function g∈C, where C is the space of 2π-periodic, continuous functions on with norm ‖f‖_C∶= maxt∈|f(t)|, r,ω__ ∞,β(r=0,1,2,…) denotes those 2π-periodic, real-valued functions f on that are analytic in the strip S_β∶=｛z∈:|Imz|0, and satisfy the restriction condition: ω(f (r),·)≤ω(·). In this paper, the exact n-width of the class of functions r,ω__ ∞,β in the space C is determined.

关键词： analytic function concave modulus of continuity n-width.

Entropy number and non-linear approximations on multivariate Besov space by manifolds of finite pseudo-dimension

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Progress in Natural Science:Materials International 2006年第3期16卷 260-265页

作者： LONG Jingfan and fang gensun (School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China Department of Computer Science, Information Technology Institute, Beijing 100101, China) School of Mathematical Sciences Beijing Normal University Beijing 100875 China Department of Computer Science Information Technology Institute Beijing 100101 China

We determine the asymptotic order of entropy number and optimal non -linear approximations of anisotropic periodic Besov class of Bpθr(Td') (1≤p≤∞,1≤0≤∞) by manifolds of finite pseudo-dimension in the metric Lq... 详细信息

关键词： Pseudo-dimension anisotropic Besov class of functions entropy number nonlinear width.

AN APPLICATION OF THE SAMPLING THEOREM

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Analysis in Theory and Applications 1999年第2期15卷 84-89页

作者： Long Jingfan (1) fang gensun (1) 1. Department of Mathematics Beijing Normal University 100875 Beijing PRC

Let Bσ,p,1 0$$ It is well known that the Shannon sampling theorem plays an important role in many applied fields [1,2,7]. In this paper we give an application of sampling theorem to approximation theory.

关键词： Math AN APPLICATION OF THE SAMPLING THEOREM

N-widths on the classes of multivariate bandlimited functions

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Progress in Natural Science:Materials International 2004年第10期14卷 23-26页

作者： fang gensun and LONG Jingfan (Department of Mathematics,Beijing Normal University,Beijing100875,China) Received January30,2004 Beijing Normal Univ Dept Math Beijing 100875 Peoples R China

In this paper,the tight order on the n-widths of the classes of multivariate bandlimited functions in L p ( d ),1

关键词： n-width multivariate bandlimited function sampling theorem

The Fundamental Theorem of Algebra for Periodic Monosplines with Multiplicity Knots

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Chinese Quarterly Journal of Mathematics 1989年第2期4卷 84-93页

作者：黄达人房艮孙浙江大学北京师范大学

We establish the fundamental theorem of algebra for periodic monosplines with odd multiplicities but one. And a comparison theorem for periodic monosplines with odd multiplicities is obtained.

关键词：样条代数基本定理系数向量当且仅当求积逼近问题数学季刊连续变形可由循环排列