Parametrization of the Solution Set of a Matricial Truncated Hamburger Moment Problem by a Schur Type Algorithm

Fritzsche, Bernd; Kirstein, Bernd; Kley, Susanne; Mädler, Conrad

doi:10.1007/978-3-030-76473-9_9

Cited by 3 publications

(3 citation statements)

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“…The application of [5,Prop. 8.8] thus yields det R (z) = 0 for all z ∈ + \D and that F := −ψ R −1 belongs to R 0,q + ; (s j ) 0 j=0 , .…”

Section: (Ii) Rank φ (Z) ψ (Z)mentioning

confidence: 99%

“…In this section, we recall a parametrization of sequences of complex matrices which are related to block Hankel matrices and consider a system of matrix polynomials, which has been proved to be useful in the context of matrix versions of classical moment problems (see, e. g. [1,2,5,7]). Let (s j ) κ j=0 be a sequence of complex p × q matrices.…”

Section: H-parameters and The R-quadruple Of Matrix Polynomialsmentioning

confidence: 99%

“…q,κ , then s * j = s j for each j ∈ Z 0,κ . Now we recall the notion of the H-parameter sequence which has been proved to be useful (see, e. g. [4,5,7,16]). Definition 5.2 ([16, Def.…”

Section: H-parameters and The R-quadruple Of Matrix Polynomialsmentioning

confidence: 99%

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Weyl Sets in a Truncated Matricial Stieltjes Moment Problem

Wall

Fritzsche

Kirstein

et al. 2022

Complex Anal. Oper. Theory

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Given a point w in the open upper complex half-plane $$\Pi _{\mathord {+}}$$ Π + , we describe the set of possible values $$F_\sigma \left( {w}\right) $$ F σ w of Stieltjes transforms $$F_\sigma \left( {z}\right) :=\int _{[\alpha ,\infty )}\left( {x-z}\right) ^{-1}\sigma \left( {\textrm{d}x}\right) $$ F σ z : = ∫ [ α , ∞ ) x - z - 1 σ d x , $$z\in \Pi _{\mathord {+}}$$ z ∈ Π + , corresponding to solutions $$\sigma $$ σ to a truncated matricial Stieltjes moment problem as intersection of two matrix balls.

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“…The application of [5,Prop. 8.8] thus yields det R (z) = 0 for all z ∈ + \D and that F := −ψ R −1 belongs to R 0,q + ; (s j ) 0 j=0 , .…”

Section: (Ii) Rank φ (Z) ψ (Z)mentioning

confidence: 99%

Section: H-parameters and The R-quadruple Of Matrix Polynomialsmentioning

confidence: 99%

See 1 more Smart Citation

Weyl Sets in a Truncated Matricial Stieltjes Moment Problem

Wall

Fritzsche

Kirstein

et al. 2022

Complex Anal. Oper. Theory

Self Cite

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Weyl Sets in a Non-degenerate Truncated Matricial Hausdorff Moment Problem

Heide,

Fritzsche,

Kirstein

et al. 2024

Complex Anal. Oper. Theory

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Given a point w in the upper half-plane $$\Pi _{\mathord {+}}$$ Π + , we describe the set of all possible values F(w) of transforms $$F(z)\,{:=}\,\int _{[\alpha ,\beta ]}(x-z)^{-1}\sigma (\textrm{d}x)$$ F ( z ) : = ∫ [ α , β ] ( x - z ) - 1 σ ( d x ) , $$z\in \Pi _{\mathord {+}}$$ z ∈ Π + , corresponding to solutions $$\sigma $$ σ to a (non-degenerate) truncated matricial Hausdorff moment problem. This set turns out to be the intersection of two matrix balls the parameters of which are explicitly constructed from the given data.

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