Truncated moment problems in the class of generalized Nevanlinna functions

Vladimir Derkach; Seppo Hassi; Henk de Snoo

doi:10.1002/mana.201100268

Truncated moment problems in the class of generalized Nevanlinna functions

Vladimir Derkach^*, Seppo Hassi, Henk de Snoo

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

Truncated moment and related interpolation problems in the class of generalized Nevanlinna functions are investigated. General solvability criteria will be established and complete parametrizations of solutions are given. The framework used in the paper allows the treatment of even and odd order problems in a parallel manner. The main new results concern the case where the corresponding Hankel matrix of moments is degenerate. One of the new effects in the indefinite case is that the degenerate moment problem may have infinitely many solutions. However, with a careful application of an indefinite analogue of a step-by-step Schur algorithm a complete description of the set of solutions will be obtained.

Original language	English
Pages (from-to)	1741-1769
Number of pages	29
Journal	Mathematische Nachrichten
Volume	285
Issue number	14-15
DOIs	https://doi.org/10.1002/mana.201100268
Publication status	Published - Oct-2012

Keywords

Generalized Nevanlinna function
asymptotic expansion
moment problem
Hankel matrix
factorization
Schur-Chebyshev algorithm
MSC (2010) Primary: 30E05
Secondary: 15B57
46C20
47A57
MATRIX POLYNOMIALS
SPACE IIX
N-KAPPA
INTERPOLATION
OPERATORS
PERTURBATIONS
FACTORIZATION
RIGIDITY
SCHUR

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title = "Truncated moment problems in the class of generalized Nevanlinna functions",

abstract = "Truncated moment and related interpolation problems in the class of generalized Nevanlinna functions are investigated. General solvability criteria will be established and complete parametrizations of solutions are given. The framework used in the paper allows the treatment of even and odd order problems in a parallel manner. The main new results concern the case where the corresponding Hankel matrix of moments is degenerate. One of the new effects in the indefinite case is that the degenerate moment problem may have infinitely many solutions. However, with a careful application of an indefinite analogue of a step-by-step Schur algorithm a complete description of the set of solutions will be obtained.",

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author = "Vladimir Derkach and Seppo Hassi and {de Snoo}, Henk",

note = "Relation: http://www.rug.nl/fmns-research/bernoulli/index Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science",

year = "2012",

month = oct,

doi = "10.1002/mana.201100268",

language = "English",

volume = "285",

pages = "1741--1769",

journal = "Mathematische Nachrichten",

issn = "0025-584X",

publisher = "WILEY-V C H VERLAG GMBH",

number = "14-15",

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TY - JOUR

T1 - Truncated moment problems in the class of generalized Nevanlinna functions

AU - Derkach, Vladimir

AU - Hassi, Seppo

AU - de Snoo, Henk

N1 - Relation: http://www.rug.nl/fmns-research/bernoulli/index Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science

PY - 2012/10

Y1 - 2012/10

N2 - Truncated moment and related interpolation problems in the class of generalized Nevanlinna functions are investigated. General solvability criteria will be established and complete parametrizations of solutions are given. The framework used in the paper allows the treatment of even and odd order problems in a parallel manner. The main new results concern the case where the corresponding Hankel matrix of moments is degenerate. One of the new effects in the indefinite case is that the degenerate moment problem may have infinitely many solutions. However, with a careful application of an indefinite analogue of a step-by-step Schur algorithm a complete description of the set of solutions will be obtained.

AB - Truncated moment and related interpolation problems in the class of generalized Nevanlinna functions are investigated. General solvability criteria will be established and complete parametrizations of solutions are given. The framework used in the paper allows the treatment of even and odd order problems in a parallel manner. The main new results concern the case where the corresponding Hankel matrix of moments is degenerate. One of the new effects in the indefinite case is that the degenerate moment problem may have infinitely many solutions. However, with a careful application of an indefinite analogue of a step-by-step Schur algorithm a complete description of the set of solutions will be obtained.

KW - Generalized Nevanlinna function

KW - asymptotic expansion

KW - moment problem

KW - Hankel matrix

KW - factorization

KW - Schur-Chebyshev algorithm

KW - MSC (2010) Primary: 30E05

KW - Secondary: 15B57

KW - 46C20

KW - 47A57

KW - MATRIX POLYNOMIALS

KW - SPACE IIX

KW - N-KAPPA

KW - INTERPOLATION

KW - OPERATORS

KW - PERTURBATIONS

KW - FACTORIZATION

KW - RIGIDITY

KW - SCHUR

U2 - 10.1002/mana.201100268

DO - 10.1002/mana.201100268

M3 - Article

SN - 0025-584X

VL - 285

SP - 1741

EP - 1769

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 14-15

ER -

Truncated moment problems in the class of generalized Nevanlinna functions

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Keywords

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