The truncated Hamburger matrix moment problems in the nondegenerate and degenerate cases, and matrix continued fractions

Chen, Gong-Ning; Hu, Yongjian

doi:10.1016/s0024-3795(97)10076-3

Cited by 46 publications

(40 citation statements)

References 9 publications

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“…The investigation of this topic was initiated by V. A. Bolotnikov's paper [15] and continued in [20]. For a comprehensive treatment of the scalar case we refer to Curto/Fialkow [24].…”

Section: Hankel Nonnegative Definite Extension Of Sequences Of Complementioning

confidence: 99%

“…The paper Chen/Hu [20] contains a careful treatment of Problem (P1) and of Problem (P2) in the case of an even number m. It deals simultaneously with the nondegenerate and degenerate cases in a unified way based on the use of a Schur type algorithm involving matrix continued fractions. This Schur type algorithm is a far-reaching generalization of the classical algorithm due to R. Nevanlinna (see [80]).…”

Section: Introductionmentioning

confidence: 99%

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On Distinguished Solutions of Truncated Matricial Hamburger Moment Problems

Dyukarev

Fritzsche

Kirstein

et al. 2008

Complex Anal. Oper. Theory

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We study two slightly different versions of the truncated matricial Hamburger moment problem. A central topic is the construction and investigation of distinguished solutions of both moment problems under consideration. These solutions turn out to be nonnegative Hermitian q × q Borel measures on the real axis which are concentrated on a finite number of points. These points and the corresponding masses will be explicitly described in terms of the given data. Furthermore, we investigate a particular class of sequences (sj) ∞ j=0 of complex q × q matrices for which the corresponding infinite matricial Hamburger moment problem has a unique solution. Our approach is mainly algebraic. It is based on the use of particular matrix polynomials constructed from a nonnegative Hermitian block Hankel matrix. These matrix polynomials are immediate generalizations of the monic orthogonal matrix polynomials associated with a positive Hermitian block Hankel matrix. We generalize a classical theorem due to Kronecker on infinite Hankel matrices of finite rank to block Hankel matrices and discuss its consequences for the nonnegative Hermitian case. Mathematics Subject Classification (2000). Primary 44A60, 47A57; Secondary 30E05.

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“…The investigation of this topic was initiated by V. A. Bolotnikov's paper [15] and continued in [20]. For a comprehensive treatment of the scalar case we refer to Curto/Fialkow [24].…”

Section: Hankel Nonnegative Definite Extension Of Sequences Of Complementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Distinguished Solutions of Truncated Matricial Hamburger Moment Problems

Dyukarev

Fritzsche

Kirstein

et al. 2008

Complex Anal. Oper. Theory

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“…N. Dyukarev w x w x 2 and by V. A. Bolotnikov 3 , who gave the description of the set of all 1 Partially supported by the National Natural Science Foundation of China.…”

Section: žmentioning

confidence: 99%

A Unified Treatment for the Matrix Stieltjes Moment Problem in Both Nondegenerate and Degenerate Cases

Chen

2001

Journal of Mathematical Analysis and Applications

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“…The Nevanlinna-Pick interpolation and moment problem have been widely studied in the literature, and interconnections between these two types of interpolation problems are well recognized (see, e.g., the monographs [Akh,KrN1,BGR,FoF,Dym] and the references therein, and [KrN2,Nud1,Nud2,Kov,IvS,Sar,Bol1,Bol2,Che,ChL,ChH1,ChH2], etc. for more information).…”

Section: Introductionmentioning

confidence: 99%

Tangential Nevanlinna-Pick Interpolation and Its Connection with Hamburger Matrix Moment Problem

Yang

Chen

2004

Integr. equ. oper. theory

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This paper is concerned with the solution of a certain tangential Nevanlinna-Pick interpolation for Nevanlinna functions. We use the so-called block Hankel vector method to establish two intrinsic connections between the tangential Nevanlinna-Pick interpolation in the Nevanlinna class and the truncated Hamburger matrix moment problem associated with the block Hankel vector under consideration: one is a congruent relationship between their information matrices, and the other is a divisor-remainder connection between their solutions. These investigations generalize our previous work on the Nevanlinna-Pick interpolation and power matrix moment problem. Mathematics Subject Classification (2000). Primary 47A57; Secondary 30E05.

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The truncated Hamburger matrix moment problems in the nondegenerate and degenerate cases, and matrix continued fractions

Cited by 46 publications

References 9 publications

On Distinguished Solutions of Truncated Matricial Hamburger Moment Problems

On Distinguished Solutions of Truncated Matricial Hamburger Moment Problems

A Unified Treatment for the Matrix Stieltjes Moment Problem in Both Nondegenerate and Degenerate Cases

Tangential Nevanlinna-Pick Interpolation and Its Connection with Hamburger Matrix Moment Problem

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