The Weyl matrix balls corresponding to the matricial truncated Hamburger moment problem

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

doi:10.1016/j.laa.2022.06.003

Cited by 3 publications

(7 citation statements)

References 30 publications

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“…In [4,6,7] one can find further results concerning the R-QMP. At the end of this section we introduce a further system of matrix polynomials, which was already considered in [6,Sec. 6].…”

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

confidence: 94%

“…The second Hamburger moment problem belongs to a sequence (a j ) m−1 j=0 of modified data, which incorporates the left interval boundary α of the integral domain [α, ∞). As proved in [6], the set of values F (w) of the R-Stieltjes transforms F of the solutions σ to a considered Hamburger moment problem at a fixed point w coincides with some matrix ball, the center and left and right semi-radii of which can be explicitly expressed in terms of the prescribed data. Assigning the respective matrix ball to each of the two Hamburger moment problems allocated to the Stieltjes moment problem under consideration, it turns out that the set in question is indeed a subset of the intersection of these two matrix balls.…”

Section: Introductionmentioning

confidence: 92%

“…In [6], the Weyl matrix balls in the context of the matricial versions of the truncated Hamburger moment problem are studied and parametrized without additional assumptions (see Theorem 6.8 below). Some arguments applied there are also useful for our further considerations.…”

Section: Weyl Matrix Balls Of a Truncated Hamburger Moment Problemmentioning

confidence: 99%

“…Some arguments applied there are also useful for our further considerations. First we consider a sequence of rational matrix-valued functions which play an essential role in [6]. In view of Remark 5.7, we recall the corresponding notion.…”

Section: Weyl Matrix Balls Of a Truncated Hamburger Moment Problemmentioning

confidence: 99%

“…In Sect. 6, we recall the Weyl matrix balls (see [6,Thm. 8.7]) which are associated with a truncated matricial Hamburger moment problems.…”

Section: Introductionmentioning

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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“…In [4,6,7] one can find further results concerning the R-QMP. At the end of this section we introduce a further system of matrix polynomials, which was already considered in [6,Sec. 6].…”

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

confidence: 94%

Section: Introductionmentioning

confidence: 92%

Section: Weyl Matrix Balls Of a Truncated Hamburger Moment Problemmentioning

confidence: 99%

Section: Weyl Matrix Balls Of a Truncated Hamburger Moment Problemmentioning

confidence: 99%

“…In Sect. 6, we recall the Weyl matrix balls (see [6,Thm. 8.7]) which are associated with a truncated matricial Hamburger moment problems.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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