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N[a,b]类中Nevanlinna-Pick插值与Hausdorff矩量问题 被引量：4

THE NEVANLINNA-PICK INTERPOLATION IN CLASS N[a,b] AND HAUSDORFF MOMENT PROBLEM
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摘要 利用Hankel向量方法建立N [a ,b]类中Nevanlinna Pick插值与相关Hausdorff矩量问题解集之间的一一对应 ,从而获得前者问题的可解性准则和解的描述 . A one to one correspondence is established between the solutions to the NP problem in the class N and the solutions to the associated Hausdorff moment problem with the so called Hankel vector of the former. This enables one not only to find solvability criteria for the NP problem, but also to describe its solutions.
作者 吴化璋 陈公宁
机构地区 北京师范大学数学系
出处 《北京师范大学学报（自然科学版）》 CAS CSCD 北大核心 2002年第3期316-323,共8页 Journal of Beijing Normal University(Natural Science)
基金 国家自然科学基金资助项目 (199710 0 9)
关键词 NP问题 Hankel向量 可解性准则 解集 N[α b]类 Nevanlinna-Pick插值 Hausdorff矩量问题 NP problem class N Hankel vector Hausdorff moment problem
分类号 O174.42 [理学—基础数学]
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参考文献1

  • 1Felix Hausdorff. Momentprobleme für ein endliches Intervall.[J] 1923,Mathematische Zeitschrift(1):220～248

同被引文献18

  • 1吴化璋.S[a,b]类中边界Nevanlinna-Pick插值(Ⅱ)[J].Journal of Mathematical Research and Exposition,2004,24(3):559-568. 被引量：1
  • 2[1]NUDELMAN A A. A multipoint matrix moment problem [J]. Soviet Math. Dokl. , 1988,37: 167-170.
  • 3[2]SARASON D. Nevanlinna-Pick interpolation with boundary data [J]. Integral Equations and Operator Theory, 1998, 30: 231-250.
  • 4[3]CHEN Gong-ning, HU Yong-jian. Multiple Nevanlinna- Pick interpolation with both interior and boundary data and its connection with the power moment problem [J]. Linear Algebra and Appl. , 2001,323; 167-194.
  • 5[4]KREIN M G, NUDELMAN A A. The Markov Moment Problem and Extremal Problems [M]. Transl.Math. Monographs 50, Amer. Math. Soc. , Providence, RI, 1977.
  • 6[5]CHEN Gong-ning, ZHAO Bing, ZHANG Hui-ping. The general rational interpolation problem in the scalar case and its Hankel vector [J]. Linear Algebra Appl. , 1996, 244: 165-201.
  • 7[6]KREIN M G. The description of all solutions of the truncated power moment problem and some problems of operator theory [J]. Mat. Issled. , 1967, 2: 114-132; English transl. , Amer. Math. Soc. transl. ,1970,95(2) : 219-234.
  • 8Shvetsov K I. On Hamburger's moment problem with the supplementary requrement that masses are absent on a given interval. Commun Soc Math Kharkov, 1939, 16: 121-128
  • 9Allaway Wm R, Liu Xing. Characterizations for the existence of a solution to the moment problem on a finite number intervals, in Topics in Polynomials of One and Several Variables and Their Applications. New Jersey: World Scientific Publ Co., 1993.9-33
  • 10Allen G D, Narcowich F J. R-Operators Ⅰ. Representation theory and applications. Indiana U Math J, 1976, 25: 945-963

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北京师范大学学报（自然科学版）
2002年 第3期

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